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<h2 class="hd hd-2 unit-title">Dipole Above a Ring of Current</h2>
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Dipole Above a Ring of Current - part a.
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<p>
A ring of radius [mathjaxinline]R[/mathjaxinline], located in the [mathjaxinline]xy[/mathjaxinline]-plane and centered about the [mathjaxinline]z[/mathjaxinline]-axis, carries a current [mathjaxinline]I[/mathjaxinline] directed clockwise as seen from above, (Figure (a)). </p>
<p><b class="bfseries">(Part a)</b>Determine the direction and magnitude of the magnetic field at a point [mathjaxinline]P[/mathjaxinline] that lies on the positive [mathjaxinline]z[/mathjaxinline]-axis a distance [mathjaxinline]z[/mathjaxinline] from the origin. Express your answer in terms of [mathjaxinline]R[/mathjaxinline], mu_0 for [mathjaxinline]\mu _0[/mathjaxinline], [mathjaxinline]z[/mathjaxinline], [mathjaxinline]I[/mathjaxinline], and hati, hatj, and hatk for [mathjaxinline]\hat{\mathbf{i}}[/mathjaxinline], [mathjaxinline]\hat{\mathbf{j}}[/mathjaxinline], and [mathjaxinline]\hat{\mathbf{k}}[/mathjaxinline], respectively, as needed. </p>
<p>
<p style="display:inline">[mathjaxinline]\vec{\mathbf{B}}(P)[/mathjaxinline] = </p>
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Dipole Above a Ring of Current - part b.
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A point-like magnetic dipole is now placed at the point [mathjaxinline]P[/mathjaxinline]. The dipole moment is given by [mathjaxinline]\vec{\mu }=\mu _ z \left(-\hat{\mathbf{k}}\right)[/mathjaxinline], where [mathjaxinline]\mu _ z&gt;0[/mathjaxinline], (Figure (b)). </p>
<p><b class="bfseries">(Part b)</b> What is the <i class="itshape">direction</i> of the force on the dipole? </p>
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<text>force is 0</text>
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Dipole Above a Ring of Current - part c.
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<p><b class="bfseries">(Part c)</b> Determine an expression for the <i class="itshape">magnitude</i> of the force on the dipole. Express your answer in terms of [mathjaxinline]R[/mathjaxinline], [mathjaxinline]\mu _0[/mathjaxinline], [mathjaxinline]z[/mathjaxinline], [mathjaxinline]I[/mathjaxinline], and [mathjaxinline]\mu _ z[/mathjaxinline] as needed. </p>
<p>
<p style="display:inline">[mathjaxinline]|F_ z|[/mathjaxinline] = </p>
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<h2 class="hd hd-2 unit-title">Dipole in Different Fields</h2>
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Dipole in Different Fields
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Consider a small magnetic dipole at the origin of the coordinate system as shown. </p>
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<p>
The dipole moment vector is given by: </p>
<table id="a0000000002" cellpadding="7" width="100%" cellspacing="0" class="eqnarray" style="table-layout:auto">
<tr id="a0000000003">
<td style="width:40%; border:none">&#160;</td>
<td style="vertical-align:middle; text-align:right; border:none">
[mathjaxinline]\displaystyle \vec{\mu }=\mu _ C\left(\hat{i}+\hat{j}\right)[/mathjaxinline]
</td>
<td style="width:40%; border:none">&#160;</td>
<td style="width:20%; border:none" class="eqnnum">&#160;</td>
</tr>
</table>
<p>
where [mathjaxinline]\mu _ C[/mathjaxinline] is a positive constant. </p>
<p>
This dipole is exposed to the following magnetic fields where [mathjaxinline]B_0[/mathjaxinline] is in all cases a positive constant of units of Tesla: </p>
<p><b class="bfseries">Case A:</b> [mathjaxinline]\vec{B} = B_0 \hat{j}[/mathjaxinline] </p>
<p><b class="bfseries">Case B:</b> [mathjaxinline]\vec{B} = -B_0\left(\hat{i}+ \hat{j}\right)[/mathjaxinline] </p>
<p><b class="bfseries">Case C:</b> [mathjaxinline]\vec{B} = B_0 \dfrac {x}{d} \hat{i}[/mathjaxinline] </p>
<p><b class="bfseries">Case D:</b> [mathjaxinline]\vec{B} = -B_0 \dfrac {x}{d} \hat{j}[/mathjaxinline] </p>
<p><b class="bfseries">Case E:</b> [mathjaxinline]\vec{B} = B_0 \dfrac {x^2}{d^2} \hat{j}[/mathjaxinline] </p>
<p><b class="bfseries">Case F:</b> [mathjaxinline]\vec{B} = B_0 \left(\dfrac {x_0}{d}-\dfrac {x^2}{d^2}\right) \hat{j}[/mathjaxinline] </p>
<p>
Note that [mathjaxinline]x_0[/mathjaxinline], and [mathjaxinline]d[/mathjaxinline] are positive constant of units of meters, and [mathjaxinline]x[/mathjaxinline] is the [mathjaxinline]x[/mathjaxinline] component of a point in the ([mathjaxinline]x,y[/mathjaxinline]) plane. The dipole is held fixed so that it cannot rotate or move. </p>
<p>
As you answer the following questions, think about how your answer would change if the dipole <i class="it">could</i> rotate or was in at a slightly different position or angle. These alternatives will be discussed in the solutions. </p>
<p><b class="bfseries">(Part 1)</b> In which case (or cases) will the dipole experience a torque that tends to rotate it in the counterclockwise direction as viewed from [mathjaxinline]+z[/mathjaxinline]? <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_pset7_7_2_1">
<fieldset aria-describedby="status_pset7_7_2_1">
<div class="field">
<input type="checkbox" name="input_pset7_7_2_1[]" id="input_pset7_7_2_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="pset7_7_2_1-choice_0-label" for="input_pset7_7_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_pset7_7_2_1"> <text>A</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_2_1[]" id="input_pset7_7_2_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="pset7_7_2_1-choice_1-label" for="input_pset7_7_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_pset7_7_2_1"> <text>B</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_2_1[]" id="input_pset7_7_2_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="pset7_7_2_1-choice_2-label" for="input_pset7_7_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_pset7_7_2_1"> <text>C</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_2_1[]" id="input_pset7_7_2_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="pset7_7_2_1-choice_3-label" for="input_pset7_7_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_pset7_7_2_1"> <text>D</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_2_1[]" id="input_pset7_7_2_1_choice_4" class="field-input input-checkbox" value="choice_4"/><label id="pset7_7_2_1-choice_4-label" for="input_pset7_7_2_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_pset7_7_2_1"> <text>E</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_2_1[]" id="input_pset7_7_2_1_choice_5" class="field-input input-checkbox" value="choice_5"/><label id="pset7_7_2_1-choice_5-label" for="input_pset7_7_2_1_choice_5" class="response-label field-label label-inline" aria-describedby="status_pset7_7_2_1"> <text>F</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_2_1[]" id="input_pset7_7_2_1_choice_6" class="field-input input-checkbox" value="choice_6"/><label id="pset7_7_2_1-choice_6-label" for="input_pset7_7_2_1_choice_6" class="response-label field-label label-inline" aria-describedby="status_pset7_7_2_1"> <text>None of them</text>
</label>
</div>
<span id="answer_pset7_7_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_pset7_7_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div> </p>
<p><b class="bfseries">(Part 2)</b> In which case (or cases) will the dipole experience a torque that tends to rotate it in the clockwise direction as viewed from [mathjaxinline]+z[/mathjaxinline]? <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div class="choicegroup capa_inputtype" id="inputtype_pset7_7_3_1">
<fieldset aria-describedby="status_pset7_7_3_1">
<div class="field">
<input type="checkbox" name="input_pset7_7_3_1[]" id="input_pset7_7_3_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="pset7_7_3_1-choice_0-label" for="input_pset7_7_3_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_pset7_7_3_1"> <text>A</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_3_1[]" id="input_pset7_7_3_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="pset7_7_3_1-choice_1-label" for="input_pset7_7_3_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_pset7_7_3_1"> <text>B</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_3_1[]" id="input_pset7_7_3_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="pset7_7_3_1-choice_2-label" for="input_pset7_7_3_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_pset7_7_3_1"> <text>C</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_3_1[]" id="input_pset7_7_3_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="pset7_7_3_1-choice_3-label" for="input_pset7_7_3_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_pset7_7_3_1"> <text>D</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_3_1[]" id="input_pset7_7_3_1_choice_4" class="field-input input-checkbox" value="choice_4"/><label id="pset7_7_3_1-choice_4-label" for="input_pset7_7_3_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_pset7_7_3_1"> <text>E</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_3_1[]" id="input_pset7_7_3_1_choice_5" class="field-input input-checkbox" value="choice_5"/><label id="pset7_7_3_1-choice_5-label" for="input_pset7_7_3_1_choice_5" class="response-label field-label label-inline" aria-describedby="status_pset7_7_3_1"> <text>F</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_3_1[]" id="input_pset7_7_3_1_choice_6" class="field-input input-checkbox" value="choice_6"/><label id="pset7_7_3_1-choice_6-label" for="input_pset7_7_3_1_choice_6" class="response-label field-label label-inline" aria-describedby="status_pset7_7_3_1"> <text>None of them</text>
</label>
</div>
<span id="answer_pset7_7_3_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_pset7_7_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div> </p>
<p><b class="bfseries">(Part 3)</b> In which case (or cases) will the dipole experience no torque? <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 3" role="group"><div class="choicegroup capa_inputtype" id="inputtype_pset7_7_4_1">
<fieldset aria-describedby="status_pset7_7_4_1">
<div class="field">
<input type="checkbox" name="input_pset7_7_4_1[]" id="input_pset7_7_4_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="pset7_7_4_1-choice_0-label" for="input_pset7_7_4_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_pset7_7_4_1"> <text>A</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_4_1[]" id="input_pset7_7_4_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="pset7_7_4_1-choice_1-label" for="input_pset7_7_4_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_pset7_7_4_1"> <text>B</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_4_1[]" id="input_pset7_7_4_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="pset7_7_4_1-choice_2-label" for="input_pset7_7_4_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_pset7_7_4_1"> <text>C</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_4_1[]" id="input_pset7_7_4_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="pset7_7_4_1-choice_3-label" for="input_pset7_7_4_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_pset7_7_4_1"> <text>D</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_4_1[]" id="input_pset7_7_4_1_choice_4" class="field-input input-checkbox" value="choice_4"/><label id="pset7_7_4_1-choice_4-label" for="input_pset7_7_4_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_pset7_7_4_1"> <text>E</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_4_1[]" id="input_pset7_7_4_1_choice_5" class="field-input input-checkbox" value="choice_5"/><label id="pset7_7_4_1-choice_5-label" for="input_pset7_7_4_1_choice_5" class="response-label field-label label-inline" aria-describedby="status_pset7_7_4_1"> <text>F</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_4_1[]" id="input_pset7_7_4_1_choice_6" class="field-input input-checkbox" value="choice_6"/><label id="pset7_7_4_1-choice_6-label" for="input_pset7_7_4_1_choice_6" class="response-label field-label label-inline" aria-describedby="status_pset7_7_4_1"> <text>None of them</text>
</label>
</div>
<span id="answer_pset7_7_4_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_pset7_7_4_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div> </p>
<p><b class="bfseries">(Part 4)</b> In which case (or cases) will the dipole experience a force that has a component in the [mathjaxinline]+x[/mathjaxinline] direction? <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 4" role="group"><div class="choicegroup capa_inputtype" id="inputtype_pset7_7_5_1">
<fieldset aria-describedby="status_pset7_7_5_1">
<div class="field">
<input type="checkbox" name="input_pset7_7_5_1[]" id="input_pset7_7_5_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="pset7_7_5_1-choice_0-label" for="input_pset7_7_5_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_pset7_7_5_1"> <text>A</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_5_1[]" id="input_pset7_7_5_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="pset7_7_5_1-choice_1-label" for="input_pset7_7_5_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_pset7_7_5_1"> <text>B</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_5_1[]" id="input_pset7_7_5_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="pset7_7_5_1-choice_2-label" for="input_pset7_7_5_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_pset7_7_5_1"> <text>C</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_5_1[]" id="input_pset7_7_5_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="pset7_7_5_1-choice_3-label" for="input_pset7_7_5_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_pset7_7_5_1"> <text>D</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_5_1[]" id="input_pset7_7_5_1_choice_4" class="field-input input-checkbox" value="choice_4"/><label id="pset7_7_5_1-choice_4-label" for="input_pset7_7_5_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_pset7_7_5_1"> <text>E</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_5_1[]" id="input_pset7_7_5_1_choice_5" class="field-input input-checkbox" value="choice_5"/><label id="pset7_7_5_1-choice_5-label" for="input_pset7_7_5_1_choice_5" class="response-label field-label label-inline" aria-describedby="status_pset7_7_5_1"> <text>F</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_5_1[]" id="input_pset7_7_5_1_choice_6" class="field-input input-checkbox" value="choice_6"/><label id="pset7_7_5_1-choice_6-label" for="input_pset7_7_5_1_choice_6" class="response-label field-label label-inline" aria-describedby="status_pset7_7_5_1"> <text>None of them</text>
</label>
</div>
<span id="answer_pset7_7_5_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_pset7_7_5_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div> </p>
<p><b class="bfseries">(Part 5)</b> In which case (or cases) will the dipole experience a force that has a component in the [mathjaxinline]-x[/mathjaxinline] direction? <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 5" role="group"><div class="choicegroup capa_inputtype" id="inputtype_pset7_7_6_1">
<fieldset aria-describedby="status_pset7_7_6_1">
<div class="field">
<input type="checkbox" name="input_pset7_7_6_1[]" id="input_pset7_7_6_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="pset7_7_6_1-choice_0-label" for="input_pset7_7_6_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_pset7_7_6_1"> <text>A</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_6_1[]" id="input_pset7_7_6_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="pset7_7_6_1-choice_1-label" for="input_pset7_7_6_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_pset7_7_6_1"> <text>B</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_6_1[]" id="input_pset7_7_6_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="pset7_7_6_1-choice_2-label" for="input_pset7_7_6_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_pset7_7_6_1"> <text>C</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_6_1[]" id="input_pset7_7_6_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="pset7_7_6_1-choice_3-label" for="input_pset7_7_6_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_pset7_7_6_1"> <text>D</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_6_1[]" id="input_pset7_7_6_1_choice_4" class="field-input input-checkbox" value="choice_4"/><label id="pset7_7_6_1-choice_4-label" for="input_pset7_7_6_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_pset7_7_6_1"> <text>E</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_6_1[]" id="input_pset7_7_6_1_choice_5" class="field-input input-checkbox" value="choice_5"/><label id="pset7_7_6_1-choice_5-label" for="input_pset7_7_6_1_choice_5" class="response-label field-label label-inline" aria-describedby="status_pset7_7_6_1"> <text>F</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_6_1[]" id="input_pset7_7_6_1_choice_6" class="field-input input-checkbox" value="choice_6"/><label id="pset7_7_6_1-choice_6-label" for="input_pset7_7_6_1_choice_6" class="response-label field-label label-inline" aria-describedby="status_pset7_7_6_1"> <text>None of them</text>
</label>
</div>
<span id="answer_pset7_7_6_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_pset7_7_6_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div> </p>
<p><b class="bfseries">(Part 6)</b> In which case (or cases) will the dipole experience a force that has a component in the [mathjaxinline]+y[/mathjaxinline] direction? <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 6" role="group"><div class="choicegroup capa_inputtype" id="inputtype_pset7_7_7_1">
<fieldset aria-describedby="status_pset7_7_7_1">
<div class="field">
<input type="checkbox" name="input_pset7_7_7_1[]" id="input_pset7_7_7_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="pset7_7_7_1-choice_0-label" for="input_pset7_7_7_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_pset7_7_7_1"> <text>A</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_7_1[]" id="input_pset7_7_7_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="pset7_7_7_1-choice_1-label" for="input_pset7_7_7_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_pset7_7_7_1"> <text>B</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_7_1[]" id="input_pset7_7_7_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="pset7_7_7_1-choice_2-label" for="input_pset7_7_7_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_pset7_7_7_1"> <text>C</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_7_1[]" id="input_pset7_7_7_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="pset7_7_7_1-choice_3-label" for="input_pset7_7_7_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_pset7_7_7_1"> <text>D</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_7_1[]" id="input_pset7_7_7_1_choice_4" class="field-input input-checkbox" value="choice_4"/><label id="pset7_7_7_1-choice_4-label" for="input_pset7_7_7_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_pset7_7_7_1"> <text>E</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pset7_7_7_1[]" id="input_pset7_7_7_1_choice_5" class="field-input input-checkbox" value="choice_5"/><label id="pset7_7_7_1-choice_5-label" for="input_pset7_7_7_1_choice_5" class="response-label field-label label-inline" aria-describedby="status_pset7_7_7_1"> <text>F</text>
</label>
</div>
<div class="field">
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<p><b class="bfseries">(Part 7)</b> In which case (or cases) will the dipole experience a force that has a component in the [mathjaxinline]-y[/mathjaxinline] direction? <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 7" role="group"><div class="choicegroup capa_inputtype" id="inputtype_pset7_7_8_1">
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<input type="checkbox" name="input_pset7_7_8_1[]" id="input_pset7_7_8_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="pset7_7_8_1-choice_0-label" for="input_pset7_7_8_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_pset7_7_8_1"> <text>A</text>
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<p><b class="bfseries">(Part 8)</b> In which case (or cases) will the dipole experience no force? <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 8" role="group"><div class="choicegroup capa_inputtype" id="inputtype_pset7_7_9_1">
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<h2 class="hd hd-2 unit-title">Making a Magnetic Moment</h2>
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Making a Magnetic Moment
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You are given a wire of length [mathjaxinline]\ell[/mathjaxinline], though which you can run a fixed current [mathjaxinline]i[/mathjaxinline]. Which of the following configurations will give the largest magnitude of magnetic dipole moment? </p>
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<text> A square of sides [mathjaxinline]\dfrac {\ell }{4}[/mathjaxinline]</text>
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<text> A circle of radius [mathjaxinline]\dfrac {\ell }{2\pi }[/mathjaxinline]</text>
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<text> A rectangle of sides [mathjaxinline]\dfrac {\ell }{10}[/mathjaxinline] and [mathjaxinline]\dfrac {4\ell }{10}[/mathjaxinline]</text>
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<text> All of these give the same magnetic dipole moment</text>
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<text> Two of these give the same largest magnetic dipole moment</text>
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