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<p>Just like electric dipoles, magnetic dipoles turn to align with an external magnetic field and feel forces in non-uniform fields.</p>
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<li><a href="https://openlearninglibrary.mit.edu/courses/course-v1:MITx+8.02.2x+2T2018/pdfbook/0/#viewer-frame" target="[object Object]">Chapter 8.4: Torque and Force on a Dipole</a></li>
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Dipole in Uniform Field
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<p>
Starting from rest, a current ring in a uniform magnetic field (with coil orientation and current flow as shown above) will: </p>
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<text> rotate clockwise, not translate</text>
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<text> translate to the left, not rotate</text>
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<h2 class="hd hd-2 unit-title">L20Q2: Magnetic Dipole in the Field Produced by Two Coils</h2>
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Magnetic Dipole in the Field Produced by Two Coils
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Consider the two concentric coils in the figure. The current in the top coil flows in the same direction as the current in the bottom coil. A dipole (shown schematically by the red circle) is initially located above the two coils, centered on the axis of the coils (which we call the [mathjaxinline]z[/mathjaxinline] direction), and pointing just a few degrees away from the [mathjaxinline]x[/mathjaxinline] axis (and therefore a few degrees away from being perpendicular to the magnetic field). In this orientation, the dipole will feel: </p>
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<text> a force but not a torque.</text>
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<text> a torque but not a force.</text>
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<text> both a torque and a force.</text>
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<h2 class="hd hd-2 unit-title">L20v4: Worked Example - Force on a Magnetic Dipole</h2>
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<p><b>Gradient.</b></p><p>Consider a scalar function \(f(x,y,z)\). The gradient of \(f\), \(\vec{\nabla}f\), is the vector given by:</p><p>
\[\vec{\nabla} f= \frac{\partial f}{\partial x}\hat{i} + \frac{\partial f}{\partial y}\hat{j} + \frac{\partial f}{\partial z}\hat{k}\]
</p><p> If the function only depends on \(x\), the gradient of the function is a vector with only an \(x\)-component:
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\[\vec{\nabla} f= \frac{df}{d x}\hat{i}\]
</p><p> where the partial derivative with respect to \(x\) is now the derivative with respect to \(x\).</p>
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A semicircular loop and infinite wire
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<p>
An infinite wire carries a current [mathjaxinline]I_1[/mathjaxinline]. A semicircular conducting loop with current [mathjaxinline]I_2[/mathjaxinline] is placed near the long wire as shown. In this configuration, the semicircular loop will <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_checkpoint_w8_2_2_1">
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<input type="radio" name="input_checkpoint_w8_2_2_1" id="input_checkpoint_w8_2_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="checkpoint_w8_2_2_1-choice_1-label" for="input_checkpoint_w8_2_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w8_2_2_1"> <text> experience no torque and no force</text>
</label>
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<input type="radio" name="input_checkpoint_w8_2_2_1" id="input_checkpoint_w8_2_2_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="checkpoint_w8_2_2_1-choice_2-label" for="input_checkpoint_w8_2_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w8_2_2_1"> <text> rotate and experience a force away from the wire</text>
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<input type="radio" name="input_checkpoint_w8_2_2_1" id="input_checkpoint_w8_2_2_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="checkpoint_w8_2_2_1-choice_3-label" for="input_checkpoint_w8_2_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w8_2_2_1"> <text> rotate and experience a force towards the wire</text>
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<input type="radio" name="input_checkpoint_w8_2_2_1" id="input_checkpoint_w8_2_2_1_choice_4" class="field-input input-radio" value="choice_4"/><label id="checkpoint_w8_2_2_1-choice_4-label" for="input_checkpoint_w8_2_2_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w8_2_2_1"> <text> rotate and experience no force</text>
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<input type="radio" name="input_checkpoint_w8_2_2_1" id="input_checkpoint_w8_2_2_1_choice_5" class="field-input input-radio" value="choice_5"/><label id="checkpoint_w8_2_2_1-choice_5-label" for="input_checkpoint_w8_2_2_1_choice_5" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w8_2_2_1"> <text> experience no torque and will translate towards the wire</text>
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<h2 class="hd hd-2 unit-title">L20Q4: Force on Magnetic Dipole</h2>
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Force on a Coil
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A circular coil is placed in an external magnetic field [mathjaxinline]\vec{B}[/mathjaxinline] as shown by the blue field lines. The current in the loop, [mathjaxinline]I[/mathjaxinline]. is flowing in the direction shown (counterclockwise as viewed from above). </p>
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The current carrying coil will feel a force <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_checkpoint_w7_7_2_1">
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