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<h2> <a href="science.html"> ⇦ Back to Science chapter list</a></h2>
<section class="sv-section">
<h1>Electromagnetism</h1>
<section class="sv-section">
<h2>1. Introduction</h2>
</section> <section class="sv-section">
<h2>2. Magnetic field associated with a current</h2>
</section> <section class="sv-section">
<h2>3. Faraday's law of electromagnetic induction</h2>
<hr><section class="sv-section sv-question sv-table"><br><div class="id4408-2162">ID is: 4408 Seed is: 2162<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/6082ede9-e7b1-516f-bd16-7c851d370b67" method="POST"><span class="worked_example"><h3 class="sv-heading">Calculations with a coil rotating in a magnetic field</h3>
</span><div class="multi-part"><div class="multi-part-header">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Nov 2016 Grade 11, P1, Q9</em></span> <br>
<a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">Physical constants</a> · <a url="/info/physics-formulas" href="https://www.emas.com/info/physics-formulas">Physics formulas</a>
</p>
<p>
A square coil with <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-1-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>8&#xA0;000</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1" style="width: 2.755em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.228em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.23em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-2"><span class="mtext" id="MathJax-Span-3" style="font-family: STIXGeneral;">8 000</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>8 000</mtext></math></span></span><script type="math/tex" id="MathJax-Element-1">\text{8 000}</script></span> windings (turns) and a <strong>side length</strong> of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-2-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0,32</mtext><mtext>&#xA0;</mtext><mtext>m</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-4" style="width: 3.399em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.755em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.75em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-5"><span class="mtext" id="MathJax-Span-6" style="font-family: STIXGeneral;">0,32</span><span class="mtext" id="MathJax-Span-7" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-8" style="font-family: STIXGeneral;">m</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0,32</mtext><mtext> </mtext><mtext>m</mtext></math></span></span><script type="math/tex" id="MathJax-Element-2">\text{0,32}\ \text{m}</script></span> is rotated inside a uniform magnetic field with a field strength of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-3-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>1,6</mtext><mtext>&#xA0;</mtext><mtext>T</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-9" style="width: 2.579em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.111em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.11em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-10"><span class="mtext" id="MathJax-Span-11" style="font-family: STIXGeneral;">1,6</span><span class="mtext" id="MathJax-Span-12" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-13" style="font-family: STIXGeneral;">T</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>1,6</mtext><mtext> </mtext><mtext>T</mtext></math></span></span><script type="math/tex" id="MathJax-Element-3">\text{1,6}\ \text{T}</script></span>.
</p>
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</div>
<ol class="multi-part-entries"><li class="multi-part-entry">
<div class="problem">
<p>
Calculate the magnetic flux passing through the coil if the normal of the coil is at an angle of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-4-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>30</mtext><mtext>&#xB0;</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-14" style="width: 1.759em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.408em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.35em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-15"><span class="mtext" id="MathJax-Span-16" style="font-family: STIXGeneral;">30</span><span class="mtext" id="MathJax-Span-17" style="font-family: STIXGeneral;">°</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>30</mtext><mtext>°</mtext></math></span></span><script type="math/tex" id="MathJax-Element-4">\text{30}\text{°}</script></span> to the direction of the magnetic field.
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to <strong>three decimal places</strong>.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-5-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#x03D5;</mi><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-18" style="width: 1.994em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.642em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.58em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-19"><span class="mi" id="MathJax-Span-20" style="font-family: STIXGeneral; font-style: italic;">𝜙</span><span class="mo" id="MathJax-Span-21" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϕ</mi><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-5">\phi = </script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="0,142" size="10"><select name="question1b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="2">T·s⁻¹</option><option value="0" selected="">Wb</option><option value="3">T·m⁻¹</option><option value="1">T</option></select>
</p>
<div class="response-type">one-of<div class="response-subtype">type(numeric.abserror(0.001))</div></div></div></div></div>
</li>
<li class="multi-part-entry">
<div class="problem">
<p>
If the coil is rotated, an emf will be induced in the coil.
</p>
<p>
There is a law that describes this phenomenon. <strong>Name</strong> and <strong>state</strong> this law.
</p>
</div>
<div class="response"><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
The law is:
</p>
<div class="sv-radio-button-group" name="radio-question2a"><ul class="sv-list"><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-2aA"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-2aA" name="question2a" type="radio" value="0"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-2aA">Newton's law</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-2aB"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-2aB" name="question2a" type="radio" value="1"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-2aB">Huygens's law</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-2aC"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-2aC" name="question2a" type="radio" value="2" checked=""><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-2aC">Faraday's law</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-2aD"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-2aD" name="question2a" type="radio" value="3"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-2aD">Einstein's law</label>
</div></li><li class="sv-list-item" style="display:none;"><div class="sv-radio-button"><input id="hidden" name="question2a" type="radio" value=""></div></li></ul></div>
<p>
which states that the magnitude of the <select name="question2b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="1">number of windings</option><option value="0" selected="">induced emf</option><option value="2">cross-sectional area</option><option value="3">magnetic flux</option></select> across the ends of a conductor is <select name="question2c" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="1">inversely proportional to</option><option value="0" selected="">directly proportional to</option><option value="3">less than</option><option value="2">greater than</option></select> the <select name="question2d" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="1">change in cross-sectional area</option><option value="3">equivalent resistance</option><option value="2">induced current</option><option value="0" selected="">rate of change of magnetic flux</option></select>.
</p>
</div></div></div>
</li>
<li class="multi-part-entry">
<div class="problem">
<p>
The angle that the normal of the coil makes with the magnetic field is increased uniformly from <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-6-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>30</mtext><mtext>&#xB0;</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-22" style="width: 1.759em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.408em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.35em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-23"><span class="mtext" id="MathJax-Span-24" style="font-family: STIXGeneral;">30</span><span class="mtext" id="MathJax-Span-25" style="font-family: STIXGeneral;">°</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>30</mtext><mtext>°</mtext></math></span></span><script type="math/tex" id="MathJax-Element-6">\text{30}\text{°}</script></span> to <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-7-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>50</mtext><mtext>&#xB0;</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-26" style="width: 1.759em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.408em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.35em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-27"><span class="mtext" id="MathJax-Span-28" style="font-family: STIXGeneral;">50</span><span class="mtext" id="MathJax-Span-29" style="font-family: STIXGeneral;">°</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>50</mtext><mtext>°</mtext></math></span></span><script type="math/tex" id="MathJax-Element-7">\text{50}\text{°}</script></span> over a certain time period. This induces an emf of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-8-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>2,44</mtext><mtext>&#xA0;</mtext><mtext>V</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-30" style="width: 3.282em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.7em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-31"><span class="mtext" id="MathJax-Span-32" style="font-family: STIXGeneral;">2,44</span><span class="mtext" id="MathJax-Span-33" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-34" style="font-family: STIXGeneral;">V</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>2,44</mtext><mtext> </mtext><mtext>V</mtext></math></span></span><script type="math/tex" id="MathJax-Element-8">\text{2,44}\ \text{V}</script></span> in the coil.
</p>
<p>
The strength and direction of the magnetic field both remain constant.
</p>
<p>
Calculate the time interval (in seconds) during which the emf was produced.
</p>
<div class="note instructions"><span class="note-header">INSTRUCTIONS:</span>
<ul>
<li>
Round your answer to <strong>the nearest <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-9-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>second</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-35" style="width: 3.399em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.755em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.75em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-36"><span class="mtext" id="MathJax-Span-37" style="font-family: STIXGeneral;">second</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>second</mtext></math></span></span><script type="math/tex" id="MathJax-Element-9">\text{second}</script></span></strong>.
</li>
<li>
Use <strong>unrounded</strong> answers from previous questions. Round only your <strong>final</strong> answer.
</li>
</ul>
</div>
</div>
<div class="response"><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-10-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">&#x0394;</mi><mi>t</mi><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-38" style="width: 2.462em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.994em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.93em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-39"><span class="mi" id="MathJax-Span-40" style="font-family: STIXGeneral;">Δ</span><span class="mi" id="MathJax-Span-41" style="font-family: STIXGeneral; font-style: italic;">𝑡</span><span class="mo" id="MathJax-Span-42" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Δ</mi><mi>t</mi><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-10">\Delta t =</script></span> <input name="question3a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="120; 117; 122" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-11-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>s</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-43" style="width: 0.53em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.413em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.876em, 1000.35em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-44"><span class="mtext" id="MathJax-Span-45" style="font-family: STIXGeneral;">s</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>s</mtext></math></span></span><script type="math/tex" id="MathJax-Element-11">\text{s}</script></span>
</p>
<div class="response-type">numeric</div></div></div></div>
</li>
</ol></div><input name="response_hash" type="hidden" value="2019-04-16T17:35:20.302393"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form></div></section><section class="sv-section sv-question sv-table"><br><div class="id4408-2201">ID is: 4408 Seed is: 2201<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/6082ede9-e7b1-516f-bd16-7c851d370b67" method="POST"><span class="worked_example"><h3 class="sv-heading">Calculations with a coil rotating in a magnetic field</h3>
</span><div class="multi-part"><div class="multi-part-header">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Nov 2016 Grade 11, P1, Q9</em></span> <br>
<a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">Physical constants</a> · <a url="/info/physics-formulas" href="https://www.emas.com/info/physics-formulas">Physics formulas</a>
</p>
<p>
A square coil with <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-12-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>9&#xA0;900</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-46" style="width: 2.755em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.228em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.23em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-47"><span class="mtext" id="MathJax-Span-48" style="font-family: STIXGeneral;">9 900</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>9 900</mtext></math></span></span><script type="math/tex" id="MathJax-Element-12">\text{9 900}</script></span> windings (turns) and a <strong>side length</strong> of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-13-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0,39</mtext><mtext>&#xA0;</mtext><mtext>m</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-49" style="width: 3.399em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.755em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.75em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-50"><span class="mtext" id="MathJax-Span-51" style="font-family: STIXGeneral;">0,39</span><span class="mtext" id="MathJax-Span-52" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-53" style="font-family: STIXGeneral;">m</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0,39</mtext><mtext> </mtext><mtext>m</mtext></math></span></span><script type="math/tex" id="MathJax-Element-13">\text{0,39}\ \text{m}</script></span> is rotated inside a uniform magnetic field with a field strength of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-14-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>1,3</mtext><mtext>&#xA0;</mtext><mtext>T</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-54" style="width: 2.579em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.111em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.11em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-55"><span class="mtext" id="MathJax-Span-56" style="font-family: STIXGeneral;">1,3</span><span class="mtext" id="MathJax-Span-57" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-58" style="font-family: STIXGeneral;">T</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>1,3</mtext><mtext> </mtext><mtext>T</mtext></math></span></span><script type="math/tex" id="MathJax-Element-14">\text{1,3}\ \text{T}</script></span>.
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/4408/2201/0"><img src="./CAPS-Science-Grade-11-10-Electromagnetism_files/0(1)"></a></div>
</div>
<ol class="multi-part-entries"><li class="multi-part-entry">
<div class="problem">
<p>
Calculate the magnetic flux passing through the coil if the normal of the coil is at an angle of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-15-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext><mtext>&#xB0;</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-59" style="width: 1.115em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.881em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.82em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-60"><span class="mtext" id="MathJax-Span-61" style="font-family: STIXGeneral;">5</span><span class="mtext" id="MathJax-Span-62" style="font-family: STIXGeneral;">°</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext><mtext>°</mtext></math></span></span><script type="math/tex" id="MathJax-Element-15">\text{5}\text{°}</script></span> to the direction of the magnetic field.
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to <strong>three decimal places</strong>.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-16-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#x03D5;</mi><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-63" style="width: 1.994em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.642em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.58em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-64"><span class="mi" id="MathJax-Span-65" style="font-family: STIXGeneral; font-style: italic;">𝜙</span><span class="mo" id="MathJax-Span-66" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϕ</mi><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-16">\phi = </script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="0,197" size="10"><select name="question1b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="2">T·m⁻¹</option><option value="3">W</option><option value="1">T</option><option value="0" selected="">Wb</option></select>
</p>
<div class="response-type">one-of<div class="response-subtype">type(numeric.abserror(0.001))</div></div></div></div></div>
</li>
<li class="multi-part-entry">
<div class="problem">
<p>
If the coil is rotated, an emf will be induced in the coil.
</p>
<p>
There is a law that describes this phenomenon. <strong>Name</strong> and <strong>state</strong> this law.
</p>
</div>
<div class="response"><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
The law is:
</p>
<div class="sv-radio-button-group" name="radio-question2a"><ul class="sv-list"><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-2aA"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-2aA" name="question2a" type="radio" value="0"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-2aA">Einstein's law</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-2aB"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-2aB" name="question2a" type="radio" value="1" checked=""><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-2aB">Faraday's law</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-2aC"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-2aC" name="question2a" type="radio" value="2"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-2aC">Ohm's law</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-2aD"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-2aD" name="question2a" type="radio" value="3"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-2aD">Boyle's law</label>
</div></li><li class="sv-list-item" style="display:none;"><div class="sv-radio-button"><input id="hidden" name="question2a" type="radio" value=""></div></li></ul></div>
<p>
which states that the magnitude of the <select name="question2b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0" selected="">induced emf</option><option value="2">induced magnetic field</option><option value="1">magnetic field strength</option><option value="3">cross-sectional area</option></select> across the ends of a conductor is <select name="question2c" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="1">inversely proportional to</option><option value="0" selected="">directly proportional to</option><option value="2">greater than</option><option value="3">less than</option></select> the <select name="question2d" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="1">change in magnetic field</option><option value="2">change in cross-sectional area</option><option value="0" selected="">rate of change of magnetic flux</option><option value="3">induced current</option></select>.
</p>
</div></div></div>
</li>
<li class="multi-part-entry">
<div class="problem">
<p>
The angle that the normal of the coil makes with the magnetic field is increased uniformly from <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-17-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext><mtext>&#xB0;</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-67" style="width: 1.115em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.881em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.82em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-68"><span class="mtext" id="MathJax-Span-69" style="font-family: STIXGeneral;">5</span><span class="mtext" id="MathJax-Span-70" style="font-family: STIXGeneral;">°</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext><mtext>°</mtext></math></span></span><script type="math/tex" id="MathJax-Element-17">\text{5}\text{°}</script></span> to <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-18-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>35</mtext><mtext>&#xB0;</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-71" style="width: 1.759em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.408em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.35em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-72"><span class="mtext" id="MathJax-Span-73" style="font-family: STIXGeneral;">35</span><span class="mtext" id="MathJax-Span-74" style="font-family: STIXGeneral;">°</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>35</mtext><mtext>°</mtext></math></span></span><script type="math/tex" id="MathJax-Element-18">\text{35}\text{°}</script></span> over a certain time period. This induces an emf of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-19-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0,72</mtext><mtext>&#xA0;</mtext><mtext>V</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-75" style="width: 3.282em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.7em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-76"><span class="mtext" id="MathJax-Span-77" style="font-family: STIXGeneral;">0,72</span><span class="mtext" id="MathJax-Span-78" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-79" style="font-family: STIXGeneral;">V</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0,72</mtext><mtext> </mtext><mtext>V</mtext></math></span></span><script type="math/tex" id="MathJax-Element-19">\text{0,72}\ \text{V}</script></span> in the coil.
</p>
<p>
The strength and direction of the magnetic field both remain constant.
</p>
<p>
Calculate the time interval (in seconds) during which the emf was produced.
</p>
<div class="note instructions"><span class="note-header">INSTRUCTIONS:</span>
<ul>
<li>
Round your answer to <strong>the nearest <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-20-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>second</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-80" style="width: 3.399em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.755em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.75em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-81"><span class="mtext" id="MathJax-Span-82" style="font-family: STIXGeneral;">second</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>second</mtext></math></span></span><script type="math/tex" id="MathJax-Element-20">\text{second}</script></span></strong>.
</li>
<li>
Use <strong>unrounded</strong> answers from previous questions. Round only your <strong>final</strong> answer.
</li>
</ul>
</div>
</div>
<div class="response"><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-21-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">&#x0394;</mi><mi>t</mi><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-83" style="width: 2.462em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.994em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.93em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-84"><span class="mi" id="MathJax-Span-85" style="font-family: STIXGeneral;">Δ</span><span class="mi" id="MathJax-Span-86" style="font-family: STIXGeneral; font-style: italic;">𝑡</span><span class="mo" id="MathJax-Span-87" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Δ</mi><mi>t</mi><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-21">\Delta t =</script></span> <input name="question3a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="481; 479; 483" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-22-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>s</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-88" style="width: 0.53em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.413em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.876em, 1000.35em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-89"><span class="mtext" id="MathJax-Span-90" style="font-family: STIXGeneral;">s</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>s</mtext></math></span></span><script type="math/tex" id="MathJax-Element-22">\text{s}</script></span>
</p>
<div class="response-type">numeric</div></div></div></div>
</li>
</ol></div><input name="response_hash" type="hidden" value="2019-04-16T17:35:20.356002"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form></div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id1394-9949">ID is: 1394 Seed is: 9949<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/6082ede9-e7b1-516f-bd16-7c851d370b67" method="POST">
<span class="worked_example"><h3 class="sv-heading">The right hand grip rule</h3>
</span><div class="problem">
<p>
Anita is studying how current flowing in a wire can induce a magnetic field around the wire. She draws the following diagram of current flowing in a loop of wire:
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1394/9949/0"><img src="./CAPS-Science-Grade-11-10-Electromagnetism_files/0(2)" width="400" height="400"></a></div>
<p>
The arrows show the direction of conventional current in the wire. The <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-23-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2299;</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-91" style="width: 0.94em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.764em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.759em, 1000.71em, 2.755em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-92"><span class="mo" id="MathJax-Span-93" style="font-family: STIXGeneral;">⊙</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.139em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⊙</mo></math></span></span><script type="math/tex" id="MathJax-Element-23">\odot</script></span> and <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-24-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2297;</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-94" style="width: 0.998em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.823em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.76em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-95"><span class="mo" id="MathJax-Span-96" style="font-family: STIXGeneral;">⊗</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.075em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⊗</mo></math></span></span><script type="math/tex" id="MathJax-Element-24">\otimes</script></span> symbols show the direction of the magnetic field.
</p>
<p>
Did Anita draw the diagram correctly?
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<div class="sv-radio-button-group" name="radio-question1a"><ul class="sv-list"><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1aA"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1aA" name="question1a" type="radio" value="0" checked=""><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1aA">The diagram is correct.</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1aB"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1aB" name="question1a" type="radio" value="1"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1aB">The diagram is incorrect.</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1aC"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1aC" name="question1a" type="radio" value="2"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1aC">There is not enough information.</label>
</div></li><li class="sv-list-item" style="display:none;"><div class="sv-radio-button"><input id="hidden" name="question1a" type="radio" value=""></div></li></ul></div>
</div></div></div>
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</div></section><section class="sv-section sv-question sv-table"><br><div class="id1394-9330">ID is: 1394 Seed is: 9330<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/6082ede9-e7b1-516f-bd16-7c851d370b67" method="POST">
<span class="worked_example"><h3 class="sv-heading">The right hand grip rule</h3>
</span><div class="problem">
<p>
Tlali is studying how current flowing in a wire can induce a magnetic field around the wire. He draws the following diagram of current flowing in a loop of wire:
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1394/9330/0"><img src="./CAPS-Science-Grade-11-10-Electromagnetism_files/0(3)" width="400" height="400"></a></div>
<p>
The arrows show the direction of conventional current in the wire. The <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-25-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2299;</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-97" style="width: 0.94em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.764em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.759em, 1000.71em, 2.755em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-98"><span class="mo" id="MathJax-Span-99" style="font-family: STIXGeneral;">⊙</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.139em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⊙</mo></math></span></span><script type="math/tex" id="MathJax-Element-25">\odot</script></span> and <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-26-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2297;</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-100" style="width: 0.998em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.823em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.76em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-101"><span class="mo" id="MathJax-Span-102" style="font-family: STIXGeneral;">⊗</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.075em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⊗</mo></math></span></span><script type="math/tex" id="MathJax-Element-26">\otimes</script></span> symbols show the direction of the magnetic field.
</p>
<p>
Did Tlali draw the diagram correctly?
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<div class="sv-radio-button-group" name="radio-question1a"><ul class="sv-list"><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1aA"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1aA" name="question1a" type="radio" value="0" checked=""><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1aA">The diagram is correct.</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1aB"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1aB" name="question1a" type="radio" value="1"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1aB">The diagram is incorrect.</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1aC"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1aC" name="question1a" type="radio" value="2"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1aC">There is not enough information.</label>
</div></li><li class="sv-list-item" style="display:none;"><div class="sv-radio-button"><input id="hidden" name="question1a" type="radio" value=""></div></li></ul></div>
</div></div></div>
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</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id4399-9405">ID is: 4399 Seed is: 9405<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/6082ede9-e7b1-516f-bd16-7c851d370b67" method="POST">
<span class="worked_example"><h3 class="sv-heading">Factors affecting the induced emf in Faraday's law</h3>
</span><div class="problem">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Nov 2015 Grade 11, P1, Q10.1</em></span> <br>
<a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">Physical constants</a> · <a url="/info/physics-formulas" href="https://www.emas.com/info/physics-formulas">Physics formulas</a>
</p>
<p>
The arrangement of apparatus to demonstrate Faraday's law of electromagnetic induction is shown below.
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/4399/9405/0"><img src="./CAPS-Science-Grade-11-10-Electromagnetism_files/0(4)"></a></div>
<p>
Identify two ways in which the size of the deflection on the galvanometer can be <strong>decreased</strong>.
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
The size of the deflection on the galvanometer can be <strong>decreased</strong> by:
</p>
<div class="sv-radio-button-group" name="radio-question1a"><ul class="sv-list"><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1aA"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1aA" name="question1a" type="radio" value="0" checked=""><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1aA">moving the magnet further away from the coil</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1aB"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1aB" name="question1a" type="radio" value="1"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1aB">moving the magnet faster</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1aC"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1aC" name="question1a" type="radio" value="2"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1aC">using a coil with a lower resistance</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1aD"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1aD" name="question1a" type="radio" value="3"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1aD">moving the magnet further into the coil</label>
</div></li><li class="sv-list-item" style="display:none;"><div class="sv-radio-button"><input id="hidden" name="question1a" type="radio" value=""></div></li></ul></div>
<p>
and
</p>
<div class="sv-radio-button-group" name="radio-question1b"><ul class="sv-list"><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1bA"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1bA" name="question1b" type="radio" value="0" checked=""><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1bA">using a weaker magnet.</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1bB"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1bB" name="question1b" type="radio" value="1"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1bB">using a coil with more windings.</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1bC"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1bC" name="question1b" type="radio" value="2"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1bC">using a stronger magnet.</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1bD"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1bD" name="question1b" type="radio" value="3"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1bD">using a coil with a larger cross-sectional area.</label>
</div></li><li class="sv-list-item" style="display:none;"><div class="sv-radio-button"><input id="hidden" name="question1b" type="radio" value=""></div></li></ul></div>
</div></div></div>
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</div></section><section class="sv-section sv-question sv-table"><br><div class="id4399-5515">ID is: 4399 Seed is: 5515<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/6082ede9-e7b1-516f-bd16-7c851d370b67" method="POST">
<span class="worked_example"><h3 class="sv-heading">Factors affecting the induced emf in Faraday's law</h3>
</span><div class="problem">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Nov 2015 Grade 11, P1, Q10.1</em></span> <br>
<a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">Physical constants</a> · <a url="/info/physics-formulas" href="https://www.emas.com/info/physics-formulas">Physics formulas</a>
</p>
<p>
The arrangement of apparatus to demonstrate Faraday's law of electromagnetic induction is shown below.
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/4399/5515/0"><img src="./CAPS-Science-Grade-11-10-Electromagnetism_files/0(5)"></a></div>
<p>
Identify two ways in which the size of the deflection on the galvanometer can be <strong>increased</strong>.
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
The size of the deflection on the galvanometer can be <strong>increased</strong> by:
</p>
<div class="sv-radio-button-group" name="radio-question1a"><ul class="sv-list"><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1aA"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1aA" name="question1a" type="radio" value="0" checked=""><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1aA">using a stronger magnet</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1aB"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1aB" name="question1a" type="radio" value="1"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1aB">replacing the galvanometer with a voltmeter</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1aC"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1aC" name="question1a" type="radio" value="2"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1aC">leaving the magnet stationary inside the coil</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1aD"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1aD" name="question1a" type="radio" value="3"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1aD">moving the magnet perpendicular to the coil</label>
</div></li><li class="sv-list-item" style="display:none;"><div class="sv-radio-button"><input id="hidden" name="question1a" type="radio" value=""></div></li></ul></div>
<p>
and
</p>
<div class="sv-radio-button-group" name="radio-question1b"><ul class="sv-list"><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1bA"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1bA" name="question1b" type="radio" value="0"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1bA">using a coil with a higher resistance.</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1bB"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1bB" name="question1b" type="radio" value="1"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1bB">moving the magnet slower.</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1bC"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1bC" name="question1b" type="radio" value="2"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1bC">moving the magnet further away from the coil.</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1bD"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1bD" name="question1b" type="radio" value="3" checked=""><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1bD">using a coil with more loops.</label>
</div></li><li class="sv-list-item" style="display:none;"><div class="sv-radio-button"><input id="hidden" name="question1b" type="radio" value=""></div></li></ul></div>
</div></div></div>
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</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id4401-8447">ID is: 4401 Seed is: 8447<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/6082ede9-e7b1-516f-bd16-7c851d370b67" method="POST">
<span class="worked_example"><h3 class="sv-heading">Statement: Faraday's law</h3>
</span><div class="problem">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Nov 2015 Grade 11, P1, Q10.1</em></span> <br>
<a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">Physical constants</a> · <a url="/info/physics-formulas" href="https://www.emas.com/info/physics-formulas">Physics formulas</a>
</p>
<p>
The arrangement of apparatus to demonstrate Faraday's law of electromagnetic induction is shown below.
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/4401/8447/0"><img src="./CAPS-Science-Grade-11-10-Electromagnetism_files/0(6)"></a></div>
<p>
State <em>Faraday's law of electromagnetic induction</em> in words.
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The magnitude of the <select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="2">number of windings</option><option value="3">cross-sectional area</option><option value="1">magnetic flux</option><option value="0" selected="">induced emf</option></select> across the ends of a conductor is <select name="question1b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="1">inversely proportional to</option><option value="0" selected="">directly proportional to</option><option value="3">less than</option><option value="2">greater than</option></select> the <select name="question1c" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0" selected="">rate of change of magnetic flux</option><option value="1">equivalent resistance</option><option value="3">induced current</option><option value="2">change in magnetic field</option></select>.
</div></div></div>
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</div></section><section class="sv-section sv-question sv-table"><br><div class="id4401-9912">ID is: 4401 Seed is: 9912<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/6082ede9-e7b1-516f-bd16-7c851d370b67" method="POST">
<span class="worked_example"><h3 class="sv-heading">Statement: Faraday's law</h3>
</span><div class="problem">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Nov 2015 Grade 11, P1, Q10.1</em></span> <br>
<a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">Physical constants</a> · <a url="/info/physics-formulas" href="https://www.emas.com/info/physics-formulas">Physics formulas</a>
</p>
<p>
The arrangement of apparatus to demonstrate Faraday's law of electromagnetic induction is shown below.
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/4401/9912/0"><img src="./CAPS-Science-Grade-11-10-Electromagnetism_files/0(7)"></a></div>
<p>
State <em>Faraday's law of electromagnetic induction</em> in words.
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The magnitude of the <select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="1">magnetic flux</option><option value="3">number of windings</option><option value="2">induced magnetic field</option><option value="0" selected="">induced emf</option></select> across the ends of a conductor is <select name="question1b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0" selected="">directly proportional to</option><option value="1">inversely proportional to</option><option value="2">greater than</option><option value="3">less than</option></select> the <select name="question1c" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0" selected="">rate of change of magnetic flux</option><option value="1">equivalent resistance</option><option value="2">change in cross-sectional area</option><option value="3">induced current</option></select>.
</div></div></div>
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</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id4405-2530">ID is: 4405 Seed is: 2530<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/6082ede9-e7b1-516f-bd16-7c851d370b67" method="POST">
<span class="worked_example"><h3 class="sv-heading">Multiple choice: Applying Lenz's law</h3>
</span><div class="problem">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Nov 2015 Grade 11, P1, Q1.9</em></span> <br>
<a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">Physical constants</a> · <a url="/info/physics-formulas" href="https://www.emas.com/info/physics-formulas">Physics formulas</a>
</p>
<p>
In the diagram below, the south pole of a bar magnet is pulled away from Point <strong>Y</strong> at the end of a solenoid.
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/4405/2530/0"><img src="./CAPS-Science-Grade-11-10-Electromagnetism_files/0(8)"></a></div>
<p>
Which one of the following options about the polarity of <strong>Y</strong> and the direction of the magnetic field <strong>inside</strong> the solenoid is correct?
</p>
<table border="1"> <tbody><tr><td style="background:lightgray"></td><td style="background:lightgray;text-align:center"><strong>Polarity of Y</strong></td><td style="background:lightgray;text-align:center"><strong>Magnetic field direction inside the solenoid</strong></td></tr> <tr> <td style="background:lightgray"><strong>A</strong></td> <td>south pole</td><td><strong>X</strong> to <strong>Y</strong></td></tr><tr> <td style="background:lightgray"><strong>B</strong></td> <td>north pole</td><td><strong>X</strong> to <strong>Y</strong></td></tr><tr> <td style="background:lightgray"><strong>C</strong></td> <td>south pole</td><td><strong>Y</strong> to <strong>X</strong></td></tr><tr> <td style="background:lightgray"><strong>D</strong></td> <td>north pole</td><td><strong>Y</strong> to <strong>X</strong></td></tr></tbody></table>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">A</option><option value="1" selected="">B</option><option value="2">C</option><option value="3">D</option></select>
</div></div></div>
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</div></section><section class="sv-section sv-question sv-table"><br><div class="id4405-8297">ID is: 4405 Seed is: 8297<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/6082ede9-e7b1-516f-bd16-7c851d370b67" method="POST">
<span class="worked_example"><h3 class="sv-heading">Multiple choice: Applying Lenz's law</h3>
</span><div class="problem">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Nov 2015 Grade 11, P1, Q1.9</em></span> <br>
<a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">Physical constants</a> · <a url="/info/physics-formulas" href="https://www.emas.com/info/physics-formulas">Physics formulas</a>
</p>
<p>
In the diagram below, the south pole of a bar magnet is pulled away from Point <strong>Y</strong> at the end of a solenoid.
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/4405/8297/0"><img src="./CAPS-Science-Grade-11-10-Electromagnetism_files/0(9)"></a></div>
<p>
Which one of the following options about the polarity of <strong>Y</strong> and the direction of the magnetic field <strong>inside</strong> the solenoid is correct?
</p>
<table border="1"> <tbody><tr><td style="background:lightgray"></td><td style="background:lightgray;text-align:center"><strong>Polarity of Y</strong></td><td style="background:lightgray;text-align:center"><strong>Magnetic field direction inside the solenoid</strong></td></tr> <tr> <td style="background:lightgray"><strong>A</strong></td> <td>south pole</td><td><strong>Y</strong> to <strong>X</strong></td></tr><tr> <td style="background:lightgray"><strong>B</strong></td> <td>south pole</td><td><strong>X</strong> to <strong>Y</strong></td></tr><tr> <td style="background:lightgray"><strong>C</strong></td> <td>north pole</td><td><strong>X</strong> to <strong>Y</strong></td></tr><tr> <td style="background:lightgray"><strong>D</strong></td> <td>north pole</td><td><strong>Y</strong> to <strong>X</strong></td></tr></tbody></table>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">A</option><option value="1">B</option><option value="2" selected="">C</option><option value="3">D</option></select>
</div></div></div>
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</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id1688-5970">ID is: 1688 Seed is: 5970<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/6082ede9-e7b1-516f-bd16-7c851d370b67" method="POST"><span class="worked_example"><h3 class="sv-heading">Testing the material for a new smart phone</h3>
</span><div class="multi-part"><div class="multi-part-header">
<p>
A team of engineers is designing a new smart phone. They want to test a new type of material that will be used in the antenna of the smart phone. They set up an experiment to test the new material, by constructing a rectangular coil made from the new material.
</p>
<p>
The coil is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-27-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext><mtext>&#xA0;</mtext><mtext>cm</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-103" style="width: 2.462em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.994em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.99em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-104"><span class="mtext" id="MathJax-Span-105" style="font-family: STIXGeneral;">5</span><span class="mtext" id="MathJax-Span-106" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-107" style="font-family: STIXGeneral;">cm</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext><mtext> </mtext><mtext>cm</mtext></math></span></span><script type="math/tex" id="MathJax-Element-27">\text{5}\ \text{cm}</script></span> by <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-28-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext><mtext>&#xA0;</mtext><mtext>cm</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-108" style="width: 2.462em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.994em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.99em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-109"><span class="mtext" id="MathJax-Span-110" style="font-family: STIXGeneral;">5</span><span class="mtext" id="MathJax-Span-111" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-112" style="font-family: STIXGeneral;">cm</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext><mtext> </mtext><mtext>cm</mtext></math></span></span><script type="math/tex" id="MathJax-Element-28">\text{5}\ \text{cm}</script></span>,</span> and consists of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-29-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-113" style="width: 1.232em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.998em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.94em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-114"><span class="mn" id="MathJax-Span-115" style="font-family: STIXGeneral;">15</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math></span></span><script type="math/tex" id="MathJax-Element-29">15</script></span> windings.
</p>
<p>
The experiment involves placing the coil within a uniform magnetic field which is created by two very large electromagnets. The engineers then measure the induced emf by changing the strength of the magnetic field at a constant rate. The following diagram shows the coil and magnetic field at the start of the experiment.
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1688/5970/0"><img src="./CAPS-Science-Grade-11-10-Electromagnetism_files/0(10)"></a></div>
<p>
The following diagram shows the coil and magnetic field at the end of the measurement.
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1688/5970/1"><img src="./CAPS-Science-Grade-11-10-Electromagnetism_files/1"></a></div>
<p>
The magnitude of the magnetic field strength changes from <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-30-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>8,24</mtext><mtext>&#xA0;</mtext><mtext>T</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-116" style="width: 3.223em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.638em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.64em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-117"><span class="mtext" id="MathJax-Span-118" style="font-family: STIXGeneral;">8,24</span><span class="mtext" id="MathJax-Span-119" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-120" style="font-family: STIXGeneral;">T</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>8,24</mtext><mtext> </mtext><mtext>T</mtext></math></span></span><script type="math/tex" id="MathJax-Element-30">\text{8,24}\ \text{T}</script></span> to <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-31-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>2,3</mtext><mtext>&#xA0;</mtext><mtext>T</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-121" style="width: 2.579em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.111em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.11em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-122"><span class="mtext" id="MathJax-Span-123" style="font-family: STIXGeneral;">2,3</span><span class="mtext" id="MathJax-Span-124" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-125" style="font-family: STIXGeneral;">T</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>2,3</mtext><mtext> </mtext><mtext>T</mtext></math></span></span><script type="math/tex" id="MathJax-Element-31">\text{2,3}\ \text{T}</script></span>, with the direction of the initial and final magnetic fields as shown in the diagrams.
</p>
<p>
The change in the magnitude of the magnetic field strength takes place over a period of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-32-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>157</mtext><mtext>&#xA0;</mtext><mtext>s</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-126" style="width: 2.638em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.169em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.11em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-127"><span class="mtext" id="MathJax-Span-128" style="font-family: STIXGeneral;">157</span><span class="mtext" id="MathJax-Span-129" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-130" style="font-family: STIXGeneral;">s</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>157</mtext><mtext> </mtext><mtext>s</mtext></math></span></span><script type="math/tex" id="MathJax-Element-32">\text{157}\ \text{s}</script></span>.</span>
</p>
</div>
<ol class="multi-part-entries"><li class="multi-part-entry">
<div class="problem">
<p>
Where is the <strong>south pole</strong> of the electromagnet located?
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
The <strong>south pole</strong> of the magnet is located <select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">above</option><option value="1" selected="">below</option></select> the coil.
</p>
</div></div></div>
</li>
<li class="multi-part-entry">
<div class="problem">
<p>
What is value of the induced emf in the coil?
</p>
<div class="note instructions"><span class="note-header">INSTRUCTIONS:</span>
<ul>
<li>
Write your answer in <strong>scientific notation</strong> and then round it to <strong>two decimal places</strong>.
</li>
<li>
You must include the <strong>sign</strong> of the induced emf in your answer.
</li>
</ul>
</div>
</div>
<div class="response"><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-33-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi class="MJX-tex-caligraphic" mathvariant="script">E</mi></mrow><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-131" style="width: 1.935em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.584em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(2.169em, 1001.52em, 3.165em, -999.997em); top: -2.983em; left: 0em;"><span class="mrow" id="MathJax-Span-132"><span class="texatom" id="MathJax-Span-133"><span class="mrow" id="MathJax-Span-134"><span class="mi" id="MathJax-Span-135" style="font-family: STIXNonUnicode; font-style: italic;"><span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span></span></span><span class="mo" id="MathJax-Span-136" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span></span><span style="display: inline-block; width: 0px; height: 2.989em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi class="MJX-tex-caligraphic" mathvariant="script">E</mi></mrow><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-33">\mathcal{E} = </script></span> <input name="question2a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="1,42 * 10^-3" size="10"> <select name="question2b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0" selected="">V</option><option value="2">Wb</option><option value="3">A</option><option value="1">T</option></select>
</p>
<div class="response-type">numeric</div></div></div></div>
</li>
</ol></div><input name="response_hash" type="hidden" value="2019-04-16T17:35:20.691807"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form></div></section><section class="sv-section sv-question sv-table"><br><div class="id1688-5732">ID is: 1688 Seed is: 5732<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/6082ede9-e7b1-516f-bd16-7c851d370b67" method="POST"><span class="worked_example"><h3 class="sv-heading">Testing the material for a new smart phone</h3>
</span><div class="multi-part"><div class="multi-part-header">
<p>
A team of engineers is designing a new smart phone. They want to test a new type of material that will be used in the antenna of the smart phone. They set up an experiment to test the new material, by constructing a rectangular coil made from the new material.
</p>
<p>
The coil is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-34-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>3</mtext><mtext>&#xA0;</mtext><mtext>cm</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-137" style="width: 2.462em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.994em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.99em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-138"><span class="mtext" id="MathJax-Span-139" style="font-family: STIXGeneral;">3</span><span class="mtext" id="MathJax-Span-140" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-141" style="font-family: STIXGeneral;">cm</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>3</mtext><mtext> </mtext><mtext>cm</mtext></math></span></span><script type="math/tex" id="MathJax-Element-34">\text{3}\ \text{cm}</script></span> by <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-35-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>7</mtext><mtext>&#xA0;</mtext><mtext>cm</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-142" style="width: 2.462em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.994em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.99em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-143"><span class="mtext" id="MathJax-Span-144" style="font-family: STIXGeneral;">7</span><span class="mtext" id="MathJax-Span-145" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-146" style="font-family: STIXGeneral;">cm</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>7</mtext><mtext> </mtext><mtext>cm</mtext></math></span></span><script type="math/tex" id="MathJax-Element-35">\text{7}\ \text{cm}</script></span>,</span> and consists of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-36-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-147" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-148"><span class="mn" id="MathJax-Span-149" style="font-family: STIXGeneral;">7</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></span></span><script type="math/tex" id="MathJax-Element-36">7</script></span> windings.
</p>
<p>
The experiment involves placing the coil within a uniform magnetic field which is created by two very large electromagnets. The engineers then measure the induced emf by changing the strength of the magnetic field at a constant rate. The following diagram shows the coil and magnetic field at the start of the experiment.
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1688/5732/0"><img src="./CAPS-Science-Grade-11-10-Electromagnetism_files/0(11)"></a></div>
<p>
The following diagram shows the coil and magnetic field at the end of the measurement.
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1688/5732/1"><img src="./CAPS-Science-Grade-11-10-Electromagnetism_files/1(1)"></a></div>
<p>
The magnitude of the magnetic field strength changes from <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-37-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>7,74</mtext><mtext>&#xA0;</mtext><mtext>T</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-150" style="width: 3.223em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.638em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.64em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-151"><span class="mtext" id="MathJax-Span-152" style="font-family: STIXGeneral;">7,74</span><span class="mtext" id="MathJax-Span-153" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-154" style="font-family: STIXGeneral;">T</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>7,74</mtext><mtext> </mtext><mtext>T</mtext></math></span></span><script type="math/tex" id="MathJax-Element-37">\text{7,74}\ \text{T}</script></span> to <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-38-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>3,99</mtext><mtext>&#xA0;</mtext><mtext>T</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-155" style="width: 3.223em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.638em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.64em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-156"><span class="mtext" id="MathJax-Span-157" style="font-family: STIXGeneral;">3,99</span><span class="mtext" id="MathJax-Span-158" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-159" style="font-family: STIXGeneral;">T</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>3,99</mtext><mtext> </mtext><mtext>T</mtext></math></span></span><script type="math/tex" id="MathJax-Element-38">\text{3,99}\ \text{T}</script></span>, with the direction of the initial and final magnetic fields as shown in the diagrams.
</p>
<p>
The change in the magnitude of the magnetic field strength takes place over a period of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-39-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>32</mtext><mtext>&#xA0;</mtext><mtext>s</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-160" style="width: 1.994em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.642em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.58em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-161"><span class="mtext" id="MathJax-Span-162" style="font-family: STIXGeneral;">32</span><span class="mtext" id="MathJax-Span-163" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-164" style="font-family: STIXGeneral;">s</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>32</mtext><mtext> </mtext><mtext>s</mtext></math></span></span><script type="math/tex" id="MathJax-Element-39">\text{32}\ \text{s}</script></span>.</span>
</p>
</div>
<ol class="multi-part-entries"><li class="multi-part-entry">
<div class="problem">
<p>
Where is the <strong>south pole</strong> of the electromagnet located?
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
The <strong>south pole</strong> of the magnet is located <select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0" selected="">above</option><option value="1">below</option></select> the coil.
</p>
</div></div></div>
</li>
<li class="multi-part-entry">
<div class="problem">
<p>
What is value of the induced emf in the coil?
</p>
<div class="note instructions"><span class="note-header">INSTRUCTIONS:</span>
<ul>
<li>
Write your answer in <strong>scientific notation</strong> and then round it to <strong>two decimal places</strong>.
</li>
<li>
You must include the <strong>sign</strong> of the induced emf in your answer.
</li>
</ul>
</div>
</div>
<div class="response"><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-40-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi class="MJX-tex-caligraphic" mathvariant="script">E</mi></mrow><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-165" style="width: 1.935em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.584em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(2.169em, 1001.52em, 3.165em, -999.997em); top: -2.983em; left: 0em;"><span class="mrow" id="MathJax-Span-166"><span class="texatom" id="MathJax-Span-167"><span class="mrow" id="MathJax-Span-168"><span class="mi" id="MathJax-Span-169" style="font-family: STIXNonUnicode; font-style: italic;"><span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span></span></span><span class="mo" id="MathJax-Span-170" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span></span><span style="display: inline-block; width: 0px; height: 2.989em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi class="MJX-tex-caligraphic" mathvariant="script">E</mi></mrow><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-40">\mathcal{E} = </script></span> <input name="question2a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="1,72 * 10^-3" size="10"> <select name="question2b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="3">A</option><option value="2">Wb</option><option value="1">T</option><option value="0" selected="">V</option></select>
</p>
<div class="response-type">numeric</div></div></div></div>
</li>
</ol></div><input name="response_hash" type="hidden" value="2019-04-16T17:35:20.732685"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form></div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id4409-7077">ID is: 4409 Seed is: 7077<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/6082ede9-e7b1-516f-bd16-7c851d370b67" method="POST">
<span class="worked_example"><h3 class="sv-heading">Square and circular coils</h3>
</span><div class="problem">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Nov 2016 Grade 11, P1, Q9</em></span> <br>
<a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">Physical constants</a> · <a url="/info/physics-formulas" href="https://www.emas.com/info/physics-formulas">Physics formulas</a>
</p>
<p>
A circular coil with <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-41-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>920</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-171" style="width: 1.876em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.525em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.52em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-172"><span class="mtext" id="MathJax-Span-173" style="font-family: STIXGeneral;">920</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>920</mtext></math></span></span><script type="math/tex" id="MathJax-Element-41">\text{920}</script></span> windings (turns) and a <strong>diameter</strong> of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-42-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0,8</mtext><mtext>&#xA0;</mtext><mtext>m</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-174" style="width: 2.813em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.286em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.29em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-175"><span class="mtext" id="MathJax-Span-176" style="font-family: STIXGeneral;">0,8</span><span class="mtext" id="MathJax-Span-177" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-178" style="font-family: STIXGeneral;">m</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0,8</mtext><mtext> </mtext><mtext>m</mtext></math></span></span><script type="math/tex" id="MathJax-Element-42">\text{0,8}\ \text{m}</script></span> is rotated inside a uniform magnetic field with a field strength of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-43-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>1,0</mtext><mtext>&#xA0;</mtext><mtext>T</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-179" style="width: 2.579em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.111em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.11em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-180"><span class="mtext" id="MathJax-Span-181" style="font-family: STIXGeneral;">1,0</span><span class="mtext" id="MathJax-Span-182" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-183" style="font-family: STIXGeneral;">T</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>1,0</mtext><mtext> </mtext><mtext>T</mtext></math></span></span><script type="math/tex" id="MathJax-Element-43">\text{1,0}\ \text{T}</script></span>. It rotates through a certain angle in a fixed amount of time and an emf is induced in the coil.
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/4409/7077/0"><img src="./CAPS-Science-Grade-11-10-Electromagnetism_files/0(12)"></a></div>
<p>
The coil is <em>replaced</em> with a <strong>square</strong> coil with a <strong>side length</strong> of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-44-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0,8</mtext><mtext>&#xA0;</mtext><mtext>m</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-184" style="width: 2.813em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.286em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.29em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-185"><span class="mtext" id="MathJax-Span-186" style="font-family: STIXGeneral;">0,8</span><span class="mtext" id="MathJax-Span-187" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-188" style="font-family: STIXGeneral;">m</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0,8</mtext><mtext> </mtext><mtext>m</mtext></math></span></span><script type="math/tex" id="MathJax-Element-44">\text{0,8}\ \text{m}</script></span>.
</p>
<p>
The new square coil has the same number of windings and is made from the same material as the circular coil. The new coil is rotated between the same two magnets for the same amount of time and it starts and ends at the same angles as the circular coil.
</p>
<ol>
<li>
Will the emf induced in the square coil be <strong>greater than</strong>, <strong>less than</strong>, or <strong>equal to</strong> the emf that was induced in the circular coil?
</li>
<li>
Explain your answer.
</li>
</ol>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
<strong>1.</strong> The emf in the square coil will be <select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0" selected="">greater than</option><option value="1">less than</option><option value="2">equal to</option></select> the emf in the circular coil.
</p>
<p>
<strong>2.</strong> This is because the emf induced in a coil is
</p>
<div class="sv-radio-button-group" name="radio-question1b"><ul class="sv-list"><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1bA"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1bA" name="question1b" type="radio" value="0"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1bA">inversely proportional to area</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1bB"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1bB" name="question1b" type="radio" value="1"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1bB">directly proportional to time taken</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1bC"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1bC" name="question1b" type="radio" value="2"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1bC">inversely proportional to time taken</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1bD"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1bD" name="question1b" type="radio" value="3" checked=""><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1bD">directly proportional to area</label>
</div></li><li class="sv-list-item" style="display:none;"><div class="sv-radio-button"><input id="hidden" name="question1b" type="radio" value=""></div></li></ul></div>
<p>
and the square coil
</p>
<div class="sv-radio-button-group" name="radio-question1c"><ul class="sv-list"><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1cA"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1cA" name="question1c" type="radio" value="0"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1cA">rotates faster.</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1cB"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1cB" name="question1c" type="radio" value="1" checked=""><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1cB">has the larger area.</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1cC"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1cC" name="question1c" type="radio" value="2"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1cC">has the smaller area.</label>
</div></li><li class="sv-list-item"><div class="sv-radio-button" id="radio-node-1cD"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1cD" name="question1c" type="radio" value="3"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1cD">rotates slower.</label>
</div></li><li class="sv-list-item" style="display:none;"><div class="sv-radio-button"><input id="hidden" name="question1c" type="radio" value=""></div></li></ul></div>
</div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:35:20.757524"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id4409-5893">ID is: 4409 Seed is: 5893<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/6082ede9-e7b1-516f-bd16-7c851d370b67" method="POST">
<span class="worked_example"><h3 class="sv-heading">Square and circular coils</h3>
</span><div class="problem">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Nov 2016 Grade 11, P1, Q9</em></span> <br>
<a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">Physical constants</a> · <a url="/info/physics-formulas" href="https://www.emas.com/info/physics-formulas">Physics formulas</a>
</p>
<p>
A circular coil with <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-45-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>630</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-189" style="width: 1.876em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.525em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.52em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-190"><span class="mtext" id="MathJax-Span-191" style="font-family: STIXGeneral;">630</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>630</mtext></math></span></span><script type="math/tex" id="MathJax-Element-45">\text{630}</script></span> windings (turns) and a <strong>radius</strong> of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-46-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0,3</mtext><mtext>&#xA0;</mtext><mtext>m</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-192" style="width: 2.813em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.286em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.29em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-193"><span class="mtext" id="MathJax-Span-194" style="font-family: STIXGeneral;">0,3</span><span class="mtext" id="MathJax-Span-195" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-196" style="font-family: STIXGeneral;">m</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0,3</mtext><mtext> </mtext><mtext>m</mtext></math></span></span><script type="math/tex" id="MathJax-Element-46">\text{0,3}\ \text{m}</script></span> is rotated inside a uniform magnetic field with a field strength of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-47-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0,6</mtext><mtext>&#xA0;</mtext><mtext>T</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-197" style="width: 2.579em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.111em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.11em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-198"><span class="mtext" id="MathJax-Span-199" style="font-family: STIXGeneral;">0,6</span><span class="mtext" id="MathJax-Span-200" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-201" style="font-family: STIXGeneral;">T</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0,6</mtext><mtext> </mtext><mtext>T</mtext></math></span></span><script type="math/tex" id="MathJax-Element-47">\text{0,6}\ \text{T}</script></span>. It rotates through a certain angle in a fixed amount of time and an emf is induced in the coil.
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/4409/5893/0"><img src="./CAPS-Science-Grade-11-10-Electromagnetism_files/0(13)"></a></div>
<p>
The coil is <em>replaced</em> with a <strong>square</strong> coil with a <strong>side length</strong> of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-48-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0,3</mtext><mtext>&#xA0;</mtext><mtext>m</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-202" style="width: 2.813em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.286em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.29em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-203"><span class="mtext" id="MathJax-Span-204" style="font-family: STIXGeneral;">0,3</span><span class="mtext" id="MathJax-Span-205" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-206" style="font-family: STIXGeneral;">m</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0,3</mtext><mtext> </mtext><mtext>m</mtext></math></span></span><script type="math/tex" id="MathJax-Element-48">\text{0,3}\ \text{m}</script></span>.
</p>
<p>
The new square coil has the same number of windings and is made from the same material as the circular coil. The new coil is rotated between the same two magnets for the same amount of time and it starts and ends at the same angles as the circular coil.
</p>
<ol>
<li>
Will the emf induced in the square coil be <strong>greater than</strong>, <strong>less than</strong>, or <strong>equal to</strong> the emf that was induced in the circular coil?
</li>
<li>
Explain your answer.