<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="d0dbb7d205db11f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@vertical+block@vert-html-lesson25intro" data-init="VerticalStudentView" data-block-type="vertical" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="False" data-graded="True" data-runtime-version="1"> <h2 class="hd hd-2 unit-title">Faraday&#39;s Law and the Induced Electric Field</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.3x+1T2019+type@html+block@lesson25_01"> <div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-request-token="d0dbb7d205db11f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@html+block@lesson25_01" data-init="XBlockToXModuleShim" data-block-type="html" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="False" data-graded="True" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "HTMLModule"} </script> <p><b>Faraday's law and the induced electric field.</b></p><p> The magnetic flux through a surface can change with time if at least one of the following changes with time:</p><p><ol><li> the area of the surface.</li><li> the orientation of the surface with respect to the magnetic field.</li><li> the magnitude of the magnetic field.</li></ol></p><p>We have already seen examples of the three situations listed above. They are summarized in the figure below.</p><p><center><img src="/assets/courseware/v1/09f555734648c022a400195c92eade22/asset-v1:MITx+8.02.3x+1T2019+type@asset+block/images_html_lesson_23_03.svg" width="800"/></center></p><p>In the situations described in cases (1) and (2), the induced current can be explained by the magnetic force on the charges in the conductor due to the relative motion between the loop and the magnetic field. The work done by the magnetic force per unit charge is the motional electromotive force (emf) discussed at the beginning of this lesson:</p><p> \[ \mathcal{E} = \oint_{loop} \frac{\vec{F}_{mag}}{q} \cdot d\vec{s} = \oint_{loop} (\vec{v}\times\vec{B})\cdot d\vec{s}\] </p><p>In the situation described in case (3), there is no relative motion between the conducting loop and the magnetic field so we cannot explain the induced current by a motional electromotive force. The motion of the charges in the wire is due to the presence of an electric field. The source of this electric field is the magnetic field changing with time. In this case, the force on a charge is \(\vec{F}_{ele} = q\vec{E}\), and the emf is defined as:</p><p> \[ \mathcal{E} = \oint_{loop} \frac{\vec{F}_{ele}}{q} \cdot d\vec{s} = \oint_{loop} \vec{E}\cdot d\vec{s}\] </p><p> We notice here that the line integral of the electric field over a closed loop is <b>non-zero</b>. This electric field is different from the electric field produced by static charges where it was found to be a conservative field for which the integral around a closed loop must always equal zero.</p><p><b>Faraday's law and non-conservative electric field:</b></p><p>Faraday's law states that a time varying magnetic flux is the source of a non-conservative electric field: </p><p> \[ \mathcal{E} = \oint_{loop} \vec{E} \cdot d\vec{s}=-\frac{d\Phi_{mag}}{dt}\] </p><p> The electric field produced by the time varying magnetic flux exists at any point in space. In particular, if we place a conducting loop somewhere in space, the electric field will exert a force on the charge carriers in the conducting material, inducing a current circulating according to Lenz's law.</p><p><b>Electric field lines:</b></p><p><center><img src="/assets/courseware/v1/c012ab7059e76d23fb797b2b08436e13/asset-v1:MITx+8.02.3x+1T2019+type@asset+block/images_html_lesson_23_03b.svg" width="700"/></center></p><p> The electric field lines of the E-fields produced by time varying magnetic flux are <b>closed lines</b>. They are different from the electric field lines produced by static charges. The E-lines of electrostatic fields are open lines, they start at positive charges or at infinity, and they end at negative charges or at infinity.</p> </div> </div> <div class="vert vert-1" data-id="block-v1:MITx+8.02.3x+1T2019+type@html+block@html_8587ab087e39"> <div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-request-token="d0dbb7d205db11f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@html+block@html_8587ab087e39" data-init="XBlockToXModuleShim" data-block-type="html" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="False" data-graded="True" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "HTMLModule"} </script> <p>Textbook Links</p> <ul> <li><a href="https://openlearninglibrary.mit.edu/courses/course-v1:MITx+8.02.3x+1T2019/pdfbook/0/#viewer-frame" target="[object Object]">Chapter 10.6: Eddy Currents </a></li> </ul> </div> </div> </div> </div>

<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="d0dbb7d205db11f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@vertical+block@vert-checkpoint_w10_28" data-init="VerticalStudentView" data-block-type="vertical" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="False" data-graded="True" data-runtime-version="1"> <h2 class="hd hd-2 unit-title">L25Q1: Fields Direction</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w10_28"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="d0dbb7d205db11f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w10_28" data-init="XBlockToXModuleShim" data-block-type="problem" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="True" data-graded="True" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_checkpoint_w10_28" class="problems-wrapper" role="group" aria-labelledby="checkpoint_w10_28-problem-title" data-problem-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w10_28" data-url="/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w10_28/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;checkpoint_w10_28-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w10_28-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Field Directions. &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w10_28-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/c54bda3ea2b61148747b8e8b728695b1/asset-v1:MITx+8.02.3x+1T2019+type@asset+block/images_checkpoint_w10_28.svg&#34; width=&#34;330&#34;/&gt; &lt;/center&gt; &lt;p&gt; Electric field [mathjaxinline]\mathbf{\vec{E}}[/mathjaxinline] in the figure is the result of a time varying magnetic field [mathjaxinline]\mathbf{\vec{B}(t)}[/mathjaxinline]. In which of the following cases are the directions shown for [mathjaxinline]\mathbf{\vec{E}}[/mathjaxinline] and [mathjaxinline]\mathbf{\vec{B}}[/mathjaxinline] correct? &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_checkpoint_w10_28_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_checkpoint_w10_28_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_checkpoint_w10_28_2_1&#34; id=&#34;input_checkpoint_w10_28_2_1_choice_1&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;checkpoint_w10_28_2_1-choice_1-label&#34; for=&#34;input_checkpoint_w10_28_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_28_2_1&#34;&gt; &lt;text&gt; 1. Always&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_checkpoint_w10_28_2_1&#34; id=&#34;input_checkpoint_w10_28_2_1_choice_2&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;checkpoint_w10_28_2_1-choice_2-label&#34; for=&#34;input_checkpoint_w10_28_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_28_2_1&#34;&gt; &lt;text&gt; 2. If [mathjaxinline]|\mathbf{\vec{B}}|[/mathjaxinline] decreases with time.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_checkpoint_w10_28_2_1&#34; id=&#34;input_checkpoint_w10_28_2_1_choice_3&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;checkpoint_w10_28_2_1-choice_3-label&#34; for=&#34;input_checkpoint_w10_28_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_28_2_1&#34;&gt; &lt;text&gt; 3. If [mathjaxinline]|\mathbf{\vec{B}}|[/mathjaxinline] increases with time.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_checkpoint_w10_28_2_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_checkpoint_w10_28_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_checkpoint_w10_28_solution_1&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Field Directions.&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_checkpoint_w10_28&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_checkpoint_w10_28&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. 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<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="d0dbb7d205db11f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@vertical+block@vert-L25v01" data-init="VerticalStudentView" data-block-type="vertical" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="False" data-graded="True" data-runtime-version="1"> <h2 class="hd hd-2 unit-title">L25v1+Q2: Induced Electric Field in a Solenoid with Changing Current</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w10_13"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="d0dbb7d205db11f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w10_13" data-init="XBlockToXModuleShim" data-block-type="problem" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="True" data-graded="True" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_checkpoint_w10_13" class="problems-wrapper" role="group" aria-labelledby="checkpoint_w10_13-problem-title" data-problem-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w10_13" data-url="/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w10_13/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;checkpoint_w10_13-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w10_13-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Induced Electric Field &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w10_13-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; Consider an infinite solenoid of radius [mathjaxinline]R[/mathjaxinline]. The side view of part of the solenoid is shown in the left figure below where the axis of the solenoid is parallel to the [mathjaxinline]z[/mathjaxinline]-axis. A current [mathjaxinline]I[/mathjaxinline] is flowing in the counter-clockwise direction as viewed from the [mathjaxinline]+z[/mathjaxinline]-axis. The resulting magnetic field is uniform and parallel to the [mathjaxinline]\hat{k}[/mathjaxinline] direction inside the solenoid and zero outside. &lt;/p&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/a19b0aa20f349aba75917b692424bece/asset-v1:MITx+8.02.3x+1T2019+type@asset+block/images_checkpoint_w10_13.svg&#34; width=&#34;440&#34;/&gt; &lt;/center&gt; &lt;p&gt; If the current changes with time, the resulting magnetic field changes with time, therefore according to Faraday&#39;s law there is an induced electric field in space. The E-lines of the induced electric field are closed lines. &lt;/p&gt; &lt;p&gt; The goal of this exercise is to find the shape of these E-lines. &lt;/p&gt; &lt;p&gt; We will use the cylindrical coordinate system shown in the right figure above to describe the fields, where [mathjaxinline]r[/mathjaxinline] is the distance measured from the center of the solenoid. &lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part a)&lt;/b&gt; The electric field is a function of the position and time. We will focus here on its dependence on position. In principle, it depends on [mathjaxinline]r[/mathjaxinline], [mathjaxinline]\theta[/mathjaxinline], and [mathjaxinline]z[/mathjaxinline]: &lt;/p&gt; &lt;table id=&#34;a0000000002&#34; cellpadding=&#34;7&#34; width=&#34;100%&#34; cellspacing=&#34;0&#34; class=&#34;eqnarray&#34; style=&#34;table-layout:auto&#34;&gt; &lt;tr id=&#34;a0000000003&#34;&gt; &lt;td style=&#34;width:40%; border:none&#34;&gt;&amp;#160;&lt;/td&gt; &lt;td style=&#34;vertical-align:middle; text-align:right; border:none&#34;&gt; [mathjaxinline]\displaystyle \vec{E}(\vec{r},t)=\vec{E}(r,\theta ,z,t)[/mathjaxinline] &lt;/td&gt; &lt;td style=&#34;width:40%; border:none&#34;&gt;&amp;#160;&lt;/td&gt; &lt;td style=&#34;width:20%; border:none&#34; class=&#34;eqnnum&#34;&gt;&amp;#160;&lt;/td&gt; &lt;/tr&gt; &lt;/table&gt; &lt;p&gt; Use the symmetry of the magnetic field to choose the variables on which the magnitude of the electric field can depend. Check all that apply. &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_checkpoint_w10_13_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_checkpoint_w10_13_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_checkpoint_w10_13_2_1[]&#34; id=&#34;input_checkpoint_w10_13_2_1_choice_0&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_0&#34;/&gt;&lt;label id=&#34;checkpoint_w10_13_2_1-choice_0-label&#34; for=&#34;input_checkpoint_w10_13_2_1_choice_0&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_13_2_1&#34;&gt; &lt;text&gt;[mathjaxinline]r[/mathjaxinline]&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_checkpoint_w10_13_2_1[]&#34; id=&#34;input_checkpoint_w10_13_2_1_choice_1&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;checkpoint_w10_13_2_1-choice_1-label&#34; for=&#34;input_checkpoint_w10_13_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_13_2_1&#34;&gt; &lt;text&gt;[mathjaxinline]\theta[/mathjaxinline]&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_checkpoint_w10_13_2_1[]&#34; id=&#34;input_checkpoint_w10_13_2_1_choice_2&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;checkpoint_w10_13_2_1-choice_2-label&#34; for=&#34;input_checkpoint_w10_13_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_13_2_1&#34;&gt; &lt;text&gt;[mathjaxinline]z[/mathjaxinline]&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_checkpoint_w10_13_2_1[]&#34; id=&#34;input_checkpoint_w10_13_2_1_choice_3&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;checkpoint_w10_13_2_1-choice_3-label&#34; for=&#34;input_checkpoint_w10_13_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_13_2_1&#34;&gt; &lt;text&gt;[mathjaxinline]\vec{E}[/mathjaxinline] is uniform&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_checkpoint_w10_13_2_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_checkpoint_w10_13_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_checkpoint_w10_13_solution_1&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part b)&lt;/b&gt; The electric field vector in principle has three components. In the cylindrical coordinate system, the electric field is expressed as: &lt;/p&gt; &lt;table id=&#34;a0000000004&#34; cellpadding=&#34;7&#34; width=&#34;100%&#34; cellspacing=&#34;0&#34; class=&#34;eqnarray&#34; style=&#34;table-layout:auto&#34;&gt; &lt;tr id=&#34;a0000000005&#34;&gt; &lt;td style=&#34;width:40%; border:none&#34;&gt;&amp;#160;&lt;/td&gt; &lt;td style=&#34;vertical-align:middle; text-align:right; border:none&#34;&gt; [mathjaxinline]\displaystyle \vec{E}=E_ r\hat{r}+E_{\theta }\hat{\theta }+E_ z\hat{k}[/mathjaxinline] &lt;/td&gt; &lt;td style=&#34;width:40%; border:none&#34;&gt;&amp;#160;&lt;/td&gt; &lt;td style=&#34;width:20%; border:none&#34; class=&#34;eqnnum&#34;&gt;&amp;#160;&lt;/td&gt; &lt;/tr&gt; &lt;/table&gt; &lt;p&gt; Use the symmetry of the magnetic field to choose the non-zero electric field components. Check all that apply. &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 2&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_checkpoint_w10_13_3_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_checkpoint_w10_13_3_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_checkpoint_w10_13_3_1[]&#34; id=&#34;input_checkpoint_w10_13_3_1_choice_0&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_0&#34;/&gt;&lt;label id=&#34;checkpoint_w10_13_3_1-choice_0-label&#34; for=&#34;input_checkpoint_w10_13_3_1_choice_0&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_13_3_1&#34;&gt; &lt;text&gt;[mathjaxinline]E_ r[/mathjaxinline] radial component&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_checkpoint_w10_13_3_1[]&#34; id=&#34;input_checkpoint_w10_13_3_1_choice_1&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;checkpoint_w10_13_3_1-choice_1-label&#34; for=&#34;input_checkpoint_w10_13_3_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_13_3_1&#34;&gt; &lt;text&gt;[mathjaxinline]E_{\theta }[/mathjaxinline] tangential component&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_checkpoint_w10_13_3_1[]&#34; id=&#34;input_checkpoint_w10_13_3_1_choice_2&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;checkpoint_w10_13_3_1-choice_2-label&#34; for=&#34;input_checkpoint_w10_13_3_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_13_3_1&#34;&gt; &lt;text&gt;[mathjaxinline]E_ z[/mathjaxinline] vertical component&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_checkpoint_w10_13_3_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_checkpoint_w10_13_3_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_checkpoint_w10_13_solution_2&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Induced Electric Field&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_checkpoint_w10_13&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_checkpoint_w10_13&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. 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<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="d0dbb7d205db11f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@vertical+block@vert-L25v02" data-init="VerticalStudentView" data-block-type="vertical" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="False" data-graded="True" data-runtime-version="1"> <h2 class="hd hd-2 unit-title">L25v2: Right Hand Rule to Find the Direction of the Induced Electric Field</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.3x+1T2019+type@video+block@L25v02"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-request-token="d0dbb7d205db11f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@video+block@L25v02" data-init="XBlockToXModuleShim" data-block-type="video" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="False" data-graded="True" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Video"} </script> <h3 class="hd hd-2">L25v2: Right Hand Rule to Find the Direction of the Induced Electric Field</h3> <div id="video_L25v02" class="video closed" data-metadata='{&#34;autoAdvance&#34;: false, &#34;prioritizeHls&#34;: false, &#34;recordedYoutubeIsAvailable&#34;: true, &#34;ytTestTimeout&#34;: 1500, &#34;poster&#34;: null, &#34;streams&#34;: &#34;1.00:gr_zgvCRDl8&#34;, &#34;saveStateEnabled&#34;: false, &#34;end&#34;: 0.0, &#34;speed&#34;: null, &#34;completionPercentage&#34;: 0.95, &#34;start&#34;: 0.0, &#34;publishCompletionUrl&#34;: &#34;/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@video+block@L25v02/handler/publish_completion&#34;, &#34;duration&#34;: null, &#34;autoplay&#34;: false, &#34;savedVideoPosition&#34;: 0.0, &#34;generalSpeed&#34;: 1.0, &#34;autohideHtml5&#34;: false, &#34;ytMetadataEndpoint&#34;: &#34;&#34;, &#34;transcriptTranslationUrl&#34;: &#34;/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@video+block@L25v02/handler/transcript/translation/__lang__&#34;, &#34;showCaptions&#34;: &#34;true&#34;, &#34;completionEnabled&#34;: false, &#34;captionDataDir&#34;: null, &#34;ytApiUrl&#34;: &#34;https://www.youtube.com/iframe_api&#34;, &#34;saveStateUrl&#34;: &#34;/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@video+block@L25v02/handler/xmodule_handler/save_user_state&#34;, &#34;transcriptAvailableTranslationsUrl&#34;: &#34;/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@video+block@L25v02/handler/transcript/available_translations&#34;, &#34;sources&#34;: [], &#34;transcriptLanguages&#34;: {&#34;en&#34;: &#34;English&#34;}, &#34;transcriptLanguage&#34;: &#34;en&#34;, &#34;lmsRootURL&#34;: &#34;https://openlearninglibrary.mit.edu&#34;}' data-bumper-metadata='null' data-autoadvance-enabled="False" data-poster='null' tabindex="-1" > <div class="focus_grabber first"></div> <div class="tc-wrapper"> <div class="video-wrapper"> <span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span> <span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span> <div class="video-player-pre"></div> <div class="video-player"> <div id="L25v02"></div> <h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4> <h4 class="hd hd-4 video-hls-error is-hidden"> Your browser does not support this video format. Try using a different browser. </h4> </div> <div class="video-player-post"></div> <div class="closed-captions"></div> <div class="video-controls is-hidden"> <div> <div class="vcr"><div class="vidtime">0:00 / 0:00</div></div> <div class="secondary-controls"></div> </div> </div> </div> </div> <div class="focus_grabber last"></div> <h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_L25v02">Downloads and transcripts</h3> <div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L25v02"> <div class="wrapper-download-transcripts"> <h4 class="hd hd-5">Transcripts</h4> <a class="btn-link external-track" href="/assets/courseware/v1/db4ca367aef474944edbc2c5bb6764e8/asset-v1:MITx+8.02.3x+1T2019+type@asset+block/L25v02.srt">Download transcript</a> </div> </div> </div> </div> </div> </div> </div>

<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="d0dbb7d205db11f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@vertical+block@vert-L25v03" data-init="VerticalStudentView" data-block-type="vertical" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="False" data-graded="True" data-runtime-version="1"> <h2 class="hd hd-2 unit-title">L25v3: Lenz&#39;s Law to Find the Direction of Induced Electric Field</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.3x+1T2019+type@video+block@L25v03"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-request-token="d0dbb7d205db11f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@video+block@L25v03" data-init="XBlockToXModuleShim" data-block-type="video" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="False" data-graded="True" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Video"} </script> <h3 class="hd hd-2">L25v3: Lenz&#39;s Law to Find the Direction of Induced Electric Field</h3> <div id="video_L25v03" class="video closed" data-metadata='{&#34;autoAdvance&#34;: false, &#34;prioritizeHls&#34;: false, &#34;recordedYoutubeIsAvailable&#34;: true, &#34;ytTestTimeout&#34;: 1500, &#34;poster&#34;: null, &#34;streams&#34;: &#34;1.00:H9Kkvu4oP6o&#34;, &#34;saveStateEnabled&#34;: false, &#34;end&#34;: 0.0, &#34;speed&#34;: null, &#34;completionPercentage&#34;: 0.95, &#34;start&#34;: 0.0, &#34;publishCompletionUrl&#34;: &#34;/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@video+block@L25v03/handler/publish_completion&#34;, &#34;duration&#34;: null, &#34;autoplay&#34;: false, &#34;savedVideoPosition&#34;: 0.0, &#34;generalSpeed&#34;: 1.0, &#34;autohideHtml5&#34;: false, &#34;ytMetadataEndpoint&#34;: &#34;&#34;, &#34;transcriptTranslationUrl&#34;: &#34;/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@video+block@L25v03/handler/transcript/translation/__lang__&#34;, &#34;showCaptions&#34;: &#34;true&#34;, &#34;completionEnabled&#34;: false, &#34;captionDataDir&#34;: null, &#34;ytApiUrl&#34;: &#34;https://www.youtube.com/iframe_api&#34;, &#34;saveStateUrl&#34;: &#34;/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@video+block@L25v03/handler/xmodule_handler/save_user_state&#34;, &#34;transcriptAvailableTranslationsUrl&#34;: &#34;/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@video+block@L25v03/handler/transcript/available_translations&#34;, &#34;sources&#34;: [], &#34;transcriptLanguages&#34;: {&#34;en&#34;: &#34;English&#34;}, &#34;transcriptLanguage&#34;: &#34;en&#34;, &#34;lmsRootURL&#34;: &#34;https://openlearninglibrary.mit.edu&#34;}' data-bumper-metadata='null' data-autoadvance-enabled="False" data-poster='null' tabindex="-1" > <div class="focus_grabber first"></div> <div class="tc-wrapper"> <div class="video-wrapper"> <span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span> <span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span> <div class="video-player-pre"></div> <div class="video-player"> <div id="L25v03"></div> <h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4> <h4 class="hd hd-4 video-hls-error is-hidden"> Your browser does not support this video format. Try using a different browser. </h4> </div> <div class="video-player-post"></div> <div class="closed-captions"></div> <div class="video-controls is-hidden"> <div> <div class="vcr"><div class="vidtime">0:00 / 0:00</div></div> <div class="secondary-controls"></div> </div> </div> </div> </div> <div class="focus_grabber last"></div> <h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_L25v03">Downloads and transcripts</h3> <div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L25v03"> <div class="wrapper-download-transcripts"> <h4 class="hd hd-5">Transcripts</h4> <a class="btn-link external-track" href="/assets/courseware/v1/8ab66772102d4059d45dcf30a0b1632b/asset-v1:MITx+8.02.3x+1T2019+type@asset+block/L25v03.srt">Download transcript</a> </div> </div> </div> </div> </div> </div> </div>

<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="d0dbb7d205db11f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@vertical+block@vert-L25v04" data-init="VerticalStudentView" data-block-type="vertical" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="False" data-graded="True" data-runtime-version="1"> <h2 class="hd hd-2 unit-title">L25v4: Induced Electric Field Outside a Solenoid with Changing Current</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.3x+1T2019+type@video+block@L25v04"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-request-token="d0dbb7d205db11f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@video+block@L25v04" data-init="XBlockToXModuleShim" data-block-type="video" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="False" data-graded="True" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Video"} </script> <h3 class="hd hd-2">L25v4: Induced Electric Field Outside a Solenoid with Changing Current</h3> <div id="video_L25v04" class="video closed" data-metadata='{&#34;autoAdvance&#34;: false, &#34;prioritizeHls&#34;: false, &#34;recordedYoutubeIsAvailable&#34;: true, &#34;ytTestTimeout&#34;: 1500, &#34;poster&#34;: null, &#34;streams&#34;: &#34;1.00:KqlwNH-j23o&#34;, &#34;saveStateEnabled&#34;: false, &#34;end&#34;: 0.0, &#34;speed&#34;: null, &#34;completionPercentage&#34;: 0.95, &#34;start&#34;: 0.0, &#34;publishCompletionUrl&#34;: &#34;/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@video+block@L25v04/handler/publish_completion&#34;, &#34;duration&#34;: null, &#34;autoplay&#34;: false, &#34;savedVideoPosition&#34;: 0.0, &#34;generalSpeed&#34;: 1.0, &#34;autohideHtml5&#34;: false, &#34;ytMetadataEndpoint&#34;: &#34;&#34;, &#34;transcriptTranslationUrl&#34;: &#34;/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@video+block@L25v04/handler/transcript/translation/__lang__&#34;, &#34;showCaptions&#34;: &#34;true&#34;, &#34;completionEnabled&#34;: false, &#34;captionDataDir&#34;: null, &#34;ytApiUrl&#34;: &#34;https://www.youtube.com/iframe_api&#34;, &#34;saveStateUrl&#34;: &#34;/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@video+block@L25v04/handler/xmodule_handler/save_user_state&#34;, &#34;transcriptAvailableTranslationsUrl&#34;: &#34;/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@video+block@L25v04/handler/transcript/available_translations&#34;, &#34;sources&#34;: [], &#34;transcriptLanguages&#34;: {&#34;en&#34;: &#34;English&#34;}, &#34;transcriptLanguage&#34;: &#34;en&#34;, &#34;lmsRootURL&#34;: &#34;https://openlearninglibrary.mit.edu&#34;}' data-bumper-metadata='null' data-autoadvance-enabled="False" data-poster='null' tabindex="-1" > <div class="focus_grabber first"></div> <div class="tc-wrapper"> <div class="video-wrapper"> <span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span> <span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span> <div class="video-player-pre"></div> <div class="video-player"> <div id="L25v04"></div> <h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4> <h4 class="hd hd-4 video-hls-error is-hidden"> Your browser does not support this video format. Try using a different browser. </h4> </div> <div class="video-player-post"></div> <div class="closed-captions"></div> <div class="video-controls is-hidden"> <div> <div class="vcr"><div class="vidtime">0:00 / 0:00</div></div> <div class="secondary-controls"></div> </div> </div> </div> </div> <div class="focus_grabber last"></div> <h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_L25v04">Downloads and transcripts</h3> <div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L25v04"> <div class="wrapper-download-transcripts"> <h4 class="hd hd-5">Transcripts</h4> <a class="btn-link external-track" href="/assets/courseware/v1/7379e0916639f33b0c543b41e75d3817/asset-v1:MITx+8.02.3x+1T2019+type@asset+block/L25v04.srt">Download transcript</a> </div> </div> </div> </div> </div> </div> </div>

<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="d0dbb7d205db11f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@vertical+block@vert-onlinepset9_9" data-init="VerticalStudentView" data-block-type="vertical" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="False" data-graded="True" data-runtime-version="1"> <h2 class="hd hd-2 unit-title">L25Q3: Changing Current in a Solenoid</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@pseto9_1"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="d0dbb7d205db11f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@pseto9_1" data-init="XBlockToXModuleShim" data-block-type="problem" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="True" data-graded="True" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_pseto9_1" class="problems-wrapper" role="group" aria-labelledby="pseto9_1-problem-title" data-problem-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@pseto9_1" data-url="/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@problem+block@pseto9_1/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;pseto9_1-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@pseto9_1-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Changing Current in Solenoid &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@pseto9_1-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part a)&lt;/b&gt; The solenoid shown below has a non-constant current [mathjaxinline]I(t)[/mathjaxinline] running through it, which is increasing at a constant non-zero rate, i. e. [mathjaxinline]\dfrac {dI}{dt} &amp;gt; 0[/mathjaxinline]. The [mathjaxinline]z[/mathjaxinline]-axis is into the page. &lt;/p&gt; &lt;table style=&#34;table-layout:auto&#34;&gt; &lt;tr&gt; &lt;td style=&#34;border:none&#34;&gt; &lt;img src=&#34;/assets/courseware/v1/cac8ce82d31455ff5c253ad1261cff39/asset-v1:MITx+8.02.3x+1T2019+type@asset+block/images_Spring_2014_pset7_1-fig004.jpg&#34; width=&#34;330&#34;/&gt; &lt;/td&gt; &lt;td style=&#34;border:none&#34;&gt; &lt;img src=&#34;/assets/courseware/v1/cb5a4277f08f3c2aea7f065b1b3cad26/asset-v1:MITx+8.02.3x+1T2019+type@asset+block/images_Spring_2014_pset7_1-fig005.jpg&#34; width=&#34;330&#34;/&gt; &lt;/td&gt; &lt;/tr&gt; &lt;/table&gt; &lt;p&gt; At a point [mathjaxinline]P[/mathjaxinline] inside the solenoid there is &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_pseto9_1_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_pseto9_1_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_pseto9_1_2_1&#34; id=&#34;input_pseto9_1_2_1_choice_1&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;pseto9_1_2_1-choice_1-label&#34; for=&#34;input_pseto9_1_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pseto9_1_2_1&#34;&gt; &lt;text&gt; a) zero electric and zero magnetic field.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_pseto9_1_2_1&#34; id=&#34;input_pseto9_1_2_1_choice_2&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;pseto9_1_2_1-choice_2-label&#34; for=&#34;input_pseto9_1_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pseto9_1_2_1&#34;&gt; &lt;text&gt; b) zero electric field and magnetic field that is constant in time.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_pseto9_1_2_1&#34; id=&#34;input_pseto9_1_2_1_choice_3&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;pseto9_1_2_1-choice_3-label&#34; for=&#34;input_pseto9_1_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pseto9_1_2_1&#34;&gt; &lt;text&gt; c) zero electric field and time-changing magnetic field.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_pseto9_1_2_1&#34; id=&#34;input_pseto9_1_2_1_choice_4&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_4&#34;/&gt;&lt;label id=&#34;pseto9_1_2_1-choice_4-label&#34; for=&#34;input_pseto9_1_2_1_choice_4&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pseto9_1_2_1&#34;&gt; &lt;text&gt; d) electric field that is constant in time and zero magnetic field.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_pseto9_1_2_1&#34; id=&#34;input_pseto9_1_2_1_choice_5&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_5&#34;/&gt;&lt;label id=&#34;pseto9_1_2_1-choice_5-label&#34; for=&#34;input_pseto9_1_2_1_choice_5&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pseto9_1_2_1&#34;&gt; &lt;text&gt; e) electric and magnetic fields that are both constant in time.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_pseto9_1_2_1&#34; id=&#34;input_pseto9_1_2_1_choice_6&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_6&#34;/&gt;&lt;label id=&#34;pseto9_1_2_1-choice_6-label&#34; for=&#34;input_pseto9_1_2_1_choice_6&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pseto9_1_2_1&#34;&gt; &lt;text&gt; f) electric field that is constant in time and time-changing magnetic field.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_pseto9_1_2_1&#34; id=&#34;input_pseto9_1_2_1_choice_7&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_7&#34;/&gt;&lt;label id=&#34;pseto9_1_2_1-choice_7-label&#34; for=&#34;input_pseto9_1_2_1_choice_7&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pseto9_1_2_1&#34;&gt; &lt;text&gt; g) time-changing electric field and zero magnetic field.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_pseto9_1_2_1&#34; id=&#34;input_pseto9_1_2_1_choice_8&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_8&#34;/&gt;&lt;label id=&#34;pseto9_1_2_1-choice_8-label&#34; for=&#34;input_pseto9_1_2_1_choice_8&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pseto9_1_2_1&#34;&gt; &lt;text&gt; h) time-changing electric field and constant magnetic field.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_pseto9_1_2_1&#34; id=&#34;input_pseto9_1_2_1_choice_9&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_9&#34;/&gt;&lt;label id=&#34;pseto9_1_2_1-choice_9-label&#34; for=&#34;input_pseto9_1_2_1_choice_9&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pseto9_1_2_1&#34;&gt; &lt;text&gt; i) electric and magnetic fields that are both time-changing.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_pseto9_1_2_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_pseto9_1_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_pseto9_1_solution_1&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;p&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/92187e3e875e508a0c7874d985b893fe/asset-v1:MITx+8.02.3x+1T2019+type@asset+block/images_Spring_2014_pset7_1-fig007.png&#34; width=&#34;330&#34;/&gt; &lt;/center&gt; &lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part b)&lt;/b&gt; A stationary magnet has its north pole pointing upward. A conducting circular loop is moving downwards beneath the magnet. The induced current in the coil, as seen from above, and the force on the conducting loop due to the magnet are: &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 2&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_pseto9_1_3_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_pseto9_1_3_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_pseto9_1_3_1&#34; id=&#34;input_pseto9_1_3_1_choice_1&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;pseto9_1_3_1-choice_1-label&#34; for=&#34;input_pseto9_1_3_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pseto9_1_3_1&#34;&gt; &lt;text&gt; a) current clockwise and force up.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_pseto9_1_3_1&#34; id=&#34;input_pseto9_1_3_1_choice_2&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;pseto9_1_3_1-choice_2-label&#34; for=&#34;input_pseto9_1_3_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pseto9_1_3_1&#34;&gt; &lt;text&gt; b) current counterclockwise and force up.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_pseto9_1_3_1&#34; id=&#34;input_pseto9_1_3_1_choice_3&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;pseto9_1_3_1-choice_3-label&#34; for=&#34;input_pseto9_1_3_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pseto9_1_3_1&#34;&gt; &lt;text&gt; c) current clockwise and force down.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_pseto9_1_3_1&#34; id=&#34;input_pseto9_1_3_1_choice_4&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_4&#34;/&gt;&lt;label id=&#34;pseto9_1_3_1-choice_4-label&#34; for=&#34;input_pseto9_1_3_1_choice_4&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pseto9_1_3_1&#34;&gt; &lt;text&gt; d) current counterclockwise and force down.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_pseto9_1_3_1&#34; id=&#34;input_pseto9_1_3_1_choice_5&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_5&#34;/&gt;&lt;label id=&#34;pseto9_1_3_1-choice_5-label&#34; for=&#34;input_pseto9_1_3_1_choice_5&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pseto9_1_3_1&#34;&gt; &lt;text&gt; e) current clockwise and zero force.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_pseto9_1_3_1&#34; id=&#34;input_pseto9_1_3_1_choice_6&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_6&#34;/&gt;&lt;label id=&#34;pseto9_1_3_1-choice_6-label&#34; for=&#34;input_pseto9_1_3_1_choice_6&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pseto9_1_3_1&#34;&gt; &lt;text&gt; f) current counter clockwise and zero force.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_pseto9_1_3_1&#34; id=&#34;input_pseto9_1_3_1_choice_7&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_7&#34;/&gt;&lt;label id=&#34;pseto9_1_3_1-choice_7-label&#34; for=&#34;input_pseto9_1_3_1_choice_7&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pseto9_1_3_1&#34;&gt; &lt;text&gt; g) zero current and zero force.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_pseto9_1_3_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; 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<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="d0dbb7d205db11f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@vertical+block@vert-L25v05" data-init="VerticalStudentView" data-block-type="vertical" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="False" data-graded="True" data-runtime-version="1"> <h2 class="hd hd-2 unit-title">L25v5: Eddy Current Braking</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.3x+1T2019+type@video+block@L25v05"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-request-token="d0dbb7d205db11f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@video+block@L25v05" data-init="XBlockToXModuleShim" data-block-type="video" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="False" data-graded="True" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Video"} </script> <h3 class="hd hd-2">L25v5: Eddy Current Braking</h3> <div id="video_L25v05" class="video closed" data-metadata='{&#34;autoAdvance&#34;: false, &#34;prioritizeHls&#34;: false, &#34;recordedYoutubeIsAvailable&#34;: true, &#34;ytTestTimeout&#34;: 1500, &#34;poster&#34;: null, &#34;streams&#34;: &#34;1.00:JdW5Uu1k0d0&#34;, &#34;saveStateEnabled&#34;: false, &#34;end&#34;: 0.0, &#34;speed&#34;: null, &#34;completionPercentage&#34;: 0.95, &#34;start&#34;: 0.0, &#34;publishCompletionUrl&#34;: &#34;/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@video+block@L25v05/handler/publish_completion&#34;, &#34;duration&#34;: null, &#34;autoplay&#34;: false, &#34;savedVideoPosition&#34;: 0.0, &#34;generalSpeed&#34;: 1.0, &#34;autohideHtml5&#34;: false, &#34;ytMetadataEndpoint&#34;: &#34;&#34;, &#34;transcriptTranslationUrl&#34;: &#34;/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@video+block@L25v05/handler/transcript/translation/__lang__&#34;, &#34;showCaptions&#34;: &#34;true&#34;, &#34;completionEnabled&#34;: false, &#34;captionDataDir&#34;: null, &#34;ytApiUrl&#34;: &#34;https://www.youtube.com/iframe_api&#34;, &#34;saveStateUrl&#34;: &#34;/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@video+block@L25v05/handler/xmodule_handler/save_user_state&#34;, &#34;transcriptAvailableTranslationsUrl&#34;: &#34;/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@video+block@L25v05/handler/transcript/available_translations&#34;, &#34;sources&#34;: [], &#34;transcriptLanguages&#34;: {&#34;en&#34;: &#34;English&#34;}, &#34;transcriptLanguage&#34;: &#34;en&#34;, &#34;lmsRootURL&#34;: &#34;https://openlearninglibrary.mit.edu&#34;}' data-bumper-metadata='null' data-autoadvance-enabled="False" data-poster='null' tabindex="-1" > <div class="focus_grabber first"></div> <div class="tc-wrapper"> <div class="video-wrapper"> <span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span> <span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span> <div class="video-player-pre"></div> <div class="video-player"> <div id="L25v05"></div> <h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4> <h4 class="hd hd-4 video-hls-error is-hidden"> Your browser does not support this video format. Try using a different browser. </h4> </div> <div class="video-player-post"></div> <div class="closed-captions"></div> <div class="video-controls is-hidden"> <div> <div class="vcr"><div class="vidtime">0:00 / 0:00</div></div> <div class="secondary-controls"></div> </div> </div> </div> </div> <div class="focus_grabber last"></div> <h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_L25v05">Downloads and transcripts</h3> <div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L25v05"> <div class="wrapper-download-transcripts"> <h4 class="hd hd-5">Transcripts</h4> <a class="btn-link external-track" href="/assets/courseware/v1/a4dd12b13500db1adbcd17f58ffd028f/asset-v1:MITx+8.02.3x+1T2019+type@asset+block/L25v05.srt">Download transcript</a> </div> </div> </div> </div> </div> </div> </div>

<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="d0dbb7d205db11f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@vertical+block@checkpoint_w10_35" data-init="VerticalStudentView" data-block-type="vertical" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="False" data-graded="True" data-runtime-version="1"> <h2 class="hd hd-2 unit-title">L25Q4: Force on a Moving Rectangle and Eddy Currents</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w10_35"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="d0dbb7d205db11f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w10_35" data-init="XBlockToXModuleShim" data-block-type="problem" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="True" data-graded="True" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_checkpoint_w10_35" class="problems-wrapper" role="group" aria-labelledby="checkpoint_w10_35-problem-title" data-problem-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w10_35" data-url="/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w10_35/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="2.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;checkpoint_w10_35-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w10_35-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Force on a Moving Rectangle and Eddy Currents &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w10_35-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; Most of the examples of motional emf that we have considered until now were about conducting thin loops moving with respect to the magnetic field. Now we will examine the currents that are established in the bulk of a conductor when it moves in a magnetic field. &lt;/p&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/287de20eb137ee5d9bf17f4ee56e0904/asset-v1:MITx+8.02.3x+1T2019+type@asset+block/images_checkpoint_w10_35.svg&#34; width=&#34;440&#34;/&gt; &lt;/center&gt; &lt;p&gt; In the figure, a thin rectangular conducting sheet is moving with velocity [mathjaxinline]\mathbf{\vec{v}}[/mathjaxinline] in the [mathjaxinline]+\mathbf{\hat{i}}[/mathjaxinline] direction into a a region of uniform magnetic field of magnitude [mathjaxinline]B[/mathjaxinline] which points along the [mathjaxinline]+\mathbf{\hat{k}}[/mathjaxinline] direction. At the instant shown in the figure, the conductor has partially moved into the region of magnetic field as shown. Consider the two charges in the conductor labeled with [mathjaxinline]1[/mathjaxinline] and [mathjaxinline]2[/mathjaxinline], where [mathjaxinline]q_1=q_2=+q&amp;gt;0[/mathjaxinline]. Again, we will assume the moving charges to be positive charges consistent with the conventional current. &lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part a)&lt;/b&gt; Which of the following statements about [mathjaxinline]\mathbf{\vec{F}_1}[/mathjaxinline] and [mathjaxinline]\mathbf{\vec{F}_2}[/mathjaxinline], the forces on [mathjaxinline]q_1[/mathjaxinline] and [mathjaxinline]q_2[/mathjaxinline], respectively, are true? &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_checkpoint_w10_35_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_checkpoint_w10_35_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_checkpoint_w10_35_2_1&#34; id=&#34;input_checkpoint_w10_35_2_1_choice_1&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;checkpoint_w10_35_2_1-choice_1-label&#34; for=&#34;input_checkpoint_w10_35_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_35_2_1&#34;&gt; &lt;text&gt; [mathjaxinline]\mathbf{\vec{F}_1}[/mathjaxinline] and [mathjaxinline]\mathbf{\vec{F}_2}[/mathjaxinline] are both along the [mathjaxinline]+\mathbf{\hat{j}}[/mathjaxinline] direction&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_checkpoint_w10_35_2_1&#34; id=&#34;input_checkpoint_w10_35_2_1_choice_2&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;checkpoint_w10_35_2_1-choice_2-label&#34; for=&#34;input_checkpoint_w10_35_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_35_2_1&#34;&gt; &lt;text&gt; [mathjaxinline]\mathbf{\vec{F}_1}[/mathjaxinline] and [mathjaxinline]\mathbf{\vec{F}_2}[/mathjaxinline] are both along the [mathjaxinline]-\mathbf{\hat{j}}[/mathjaxinline] direction&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_checkpoint_w10_35_2_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_checkpoint_w10_35_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_checkpoint_w10_35_solution_1&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part b)&lt;/b&gt; Consider the 4 situations described in the figure below. &lt;/p&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/2278eac04916050d7693843646f5dacd/asset-v1:MITx+8.02.3x+1T2019+type@asset+block/images_checkpoint_w10_35b.svg&#34; width=&#34;770&#34;/&gt; &lt;/center&gt; &lt;p&gt; Which of the following statements about [mathjaxinline]I_{ind}[/mathjaxinline], the induced current on the rectangular conductor is true? &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 2&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_checkpoint_w10_35_3_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_checkpoint_w10_35_3_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_checkpoint_w10_35_3_1&#34; id=&#34;input_checkpoint_w10_35_3_1_choice_1&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;checkpoint_w10_35_3_1-choice_1-label&#34; for=&#34;input_checkpoint_w10_35_3_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_35_3_1&#34;&gt; &lt;text&gt; Figure 1. The charges move so that the resulting [mathjaxinline]I_{ind}[/mathjaxinline] flows counterclockwise.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_checkpoint_w10_35_3_1&#34; id=&#34;input_checkpoint_w10_35_3_1_choice_2&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;checkpoint_w10_35_3_1-choice_2-label&#34; for=&#34;input_checkpoint_w10_35_3_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_35_3_1&#34;&gt; &lt;text&gt; Figure 2. The charges move so that the resulting [mathjaxinline]I_{ind}[/mathjaxinline] flows clockwise.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_checkpoint_w10_35_3_1&#34; id=&#34;input_checkpoint_w10_35_3_1_choice_3&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;checkpoint_w10_35_3_1-choice_3-label&#34; for=&#34;input_checkpoint_w10_35_3_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_35_3_1&#34;&gt; &lt;text&gt; Figure 3. There is charge separation, with negative at the top and positive at the botton, and no current is induced.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_checkpoint_w10_35_3_1&#34; id=&#34;input_checkpoint_w10_35_3_1_choice_4&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_4&#34;/&gt;&lt;label id=&#34;checkpoint_w10_35_3_1-choice_4-label&#34; for=&#34;input_checkpoint_w10_35_3_1_choice_4&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_35_3_1&#34;&gt; &lt;text&gt; Figure 4. There is charge separation, with positive at the top and negative at the botton, and no current is induced.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_checkpoint_w10_35_3_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_checkpoint_w10_35_3_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_checkpoint_w10_35_solution_2&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part c)&lt;/b&gt; Assume that the conductor is moving in free space with no external forces with a uniform speed [mathjaxinline]v_0[/mathjaxinline]. When it reaches the region with magnetic field, it interacts with the field. At the instant shown in the figure, the conductor&#39;s speed is [mathjaxinline]v_1[/mathjaxinline]. Which of the following statements is true? &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 3&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_checkpoint_w10_35_4_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_checkpoint_w10_35_4_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_checkpoint_w10_35_4_1&#34; id=&#34;input_checkpoint_w10_35_4_1_choice_1&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;checkpoint_w10_35_4_1-choice_1-label&#34; for=&#34;input_checkpoint_w10_35_4_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_35_4_1&#34;&gt; &lt;text&gt; [mathjaxinline]v_1&amp;gt;v_0[/mathjaxinline], the conductor speeds up.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_checkpoint_w10_35_4_1&#34; id=&#34;input_checkpoint_w10_35_4_1_choice_2&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;checkpoint_w10_35_4_1-choice_2-label&#34; for=&#34;input_checkpoint_w10_35_4_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_35_4_1&#34;&gt; &lt;text&gt; [mathjaxinline]v_1=v_0[/mathjaxinline], the conductor moves at a constant velocity.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_checkpoint_w10_35_4_1&#34; id=&#34;input_checkpoint_w10_35_4_1_choice_3&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;checkpoint_w10_35_4_1-choice_3-label&#34; for=&#34;input_checkpoint_w10_35_4_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_35_4_1&#34;&gt; &lt;text&gt; [mathjaxinline]v_1&amp;lt;v_0[/mathjaxinline], the conductor slows down.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_checkpoint_w10_35_4_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_checkpoint_w10_35_4_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_checkpoint_w10_35_solution_3&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part d)&lt;/b&gt; Which of the following statements about the motion of the conductor in the magnetic field region are true? &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 4&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_checkpoint_w10_35_5_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_checkpoint_w10_35_5_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_checkpoint_w10_35_5_1[]&#34; id=&#34;input_checkpoint_w10_35_5_1_choice_0&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_0&#34;/&gt;&lt;label id=&#34;checkpoint_w10_35_5_1-choice_0-label&#34; for=&#34;input_checkpoint_w10_35_5_1_choice_0&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_35_5_1&#34;&gt; &lt;text&gt;The conductor slows down when it enters the B field region and it speeds up when it exits the region.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_checkpoint_w10_35_5_1[]&#34; id=&#34;input_checkpoint_w10_35_5_1_choice_1&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;checkpoint_w10_35_5_1-choice_1-label&#34; for=&#34;input_checkpoint_w10_35_5_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_35_5_1&#34;&gt; &lt;text&gt;The conductor slows down when it enters the B field region and it slows down again when it exits the B-field region.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_checkpoint_w10_35_5_1[]&#34; id=&#34;input_checkpoint_w10_35_5_1_choice_2&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;checkpoint_w10_35_5_1-choice_2-label&#34; for=&#34;input_checkpoint_w10_35_5_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_35_5_1&#34;&gt; &lt;text&gt;The conductor slows down when it enters the B field region consistent with conservation of energy.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_checkpoint_w10_35_5_1[]&#34; id=&#34;input_checkpoint_w10_35_5_1_choice_3&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;checkpoint_w10_35_5_1-choice_3-label&#34; for=&#34;input_checkpoint_w10_35_5_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_35_5_1&#34;&gt; &lt;text&gt;[mathjaxinline]I_{ind}[/mathjaxinline] produces a magnetic field in the [mathjaxinline]-\mathbf{\hat{k}}[/mathjaxinline] when the conductor enters the B field region, and it induces a magnetic field in the [mathjaxinline]+\mathbf{\hat{k}}[/mathjaxinline] when the conductor exits the B field region.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_checkpoint_w10_35_5_1[]&#34; id=&#34;input_checkpoint_w10_35_5_1_choice_4&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_4&#34;/&gt;&lt;label id=&#34;checkpoint_w10_35_5_1-choice_4-label&#34; for=&#34;input_checkpoint_w10_35_5_1_choice_4&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_35_5_1&#34;&gt; &lt;text&gt;[mathjaxinline]I_{ind}[/mathjaxinline] produces a magnetic field in the [mathjaxinline]-\mathbf{\hat{k}}[/mathjaxinline] when the conductor enters and exits the B-field region.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_checkpoint_w10_35_5_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_checkpoint_w10_35_5_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_checkpoint_w10_35_solution_4&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Force on a Moving Rectangle and Eddy Currents&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_checkpoint_w10_35&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_checkpoint_w10_35&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;checkpoint_w10_35-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;checkpoint_w10_35-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;checkpoint_w10_35-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> </div> </div>

<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="d0dbb7d205db11f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@vertical+block@vert-checkpoint_w10_31" data-init="VerticalStudentView" data-block-type="vertical" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="False" data-graded="True" data-runtime-version="1"> <h2 class="hd hd-2 unit-title">L25Q5: Forces on Moving Magnet</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w10_31"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="d0dbb7d205db11f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w10_31" data-init="XBlockToXModuleShim" data-block-type="problem" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="True" data-graded="True" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_checkpoint_w10_31" class="problems-wrapper" role="group" aria-labelledby="checkpoint_w10_31-problem-title" data-problem-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w10_31" data-url="/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w10_31/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;checkpoint_w10_31-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w10_31-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Forces on Moving Magnet &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w10_31-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/45a28943bf4ed92c9d09edc9cf7e0b56/asset-v1:MITx+8.02.3x+1T2019+type@asset+block/images_checkpoint_w10_31.svg&#34; width=&#34;440&#34;/&gt; &lt;/center&gt; &lt;p&gt; A current [mathjaxinline]I[/mathjaxinline] is flowing through the conducting loop as shown in Figure a. The magnetic field of the loop is similar to the magnetic field of the bar magnet in Figure b with &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_checkpoint_w10_31_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_checkpoint_w10_31_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_checkpoint_w10_31_2_1&#34; id=&#34;input_checkpoint_w10_31_2_1_choice_1&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;checkpoint_w10_31_2_1-choice_1-label&#34; for=&#34;input_checkpoint_w10_31_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_31_2_1&#34;&gt; &lt;text&gt; the north pole pointing up&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_checkpoint_w10_31_2_1&#34; id=&#34;input_checkpoint_w10_31_2_1_choice_2&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;checkpoint_w10_31_2_1-choice_2-label&#34; for=&#34;input_checkpoint_w10_31_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_31_2_1&#34;&gt; &lt;text&gt; the north pole pointing down&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_checkpoint_w10_31_2_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_checkpoint_w10_31_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_checkpoint_w10_31_solution_1&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part b)&lt;/b&gt; Four bar magnets are moving toward circular wire loops that are fixed in space. All the wire loops have the same radius and are made of the same material. The magnets are all identical, but they are approaching the loops at different speeds and with different orientations. &lt;/p&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/31249b63ee6f0bbc91982b5774875ad7/asset-v1:MITx+8.02.3x+1T2019+type@asset+block/images_checkpoint_w10_30.svg&#34; width=&#34;440&#34;/&gt; &lt;/center&gt; &lt;p&gt; Which of the following statements is true about the force exerted by the loop on the magnet at the instant when the magnet is to the right of the loop: &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 2&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_checkpoint_w10_31_3_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_checkpoint_w10_31_3_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_checkpoint_w10_31_3_1&#34; id=&#34;input_checkpoint_w10_31_3_1_choice_1&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;checkpoint_w10_31_3_1-choice_1-label&#34; for=&#34;input_checkpoint_w10_31_3_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_31_3_1&#34;&gt; &lt;text&gt; 1. attractive force in A and B, repulsive in C and D&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_checkpoint_w10_31_3_1&#34; id=&#34;input_checkpoint_w10_31_3_1_choice_2&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;checkpoint_w10_31_3_1-choice_2-label&#34; for=&#34;input_checkpoint_w10_31_3_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_31_3_1&#34;&gt; &lt;text&gt; 2. repulsive force in A and B, attractive in C and D&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_checkpoint_w10_31_3_1&#34; id=&#34;input_checkpoint_w10_31_3_1_choice_3&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;checkpoint_w10_31_3_1-choice_3-label&#34; for=&#34;input_checkpoint_w10_31_3_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_31_3_1&#34;&gt; &lt;text&gt; 3. attractive force in all cases&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_checkpoint_w10_31_3_1&#34; id=&#34;input_checkpoint_w10_31_3_1_choice_4&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_4&#34;/&gt;&lt;label id=&#34;checkpoint_w10_31_3_1-choice_4-label&#34; for=&#34;input_checkpoint_w10_31_3_1_choice_4&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w10_31_3_1&#34;&gt; &lt;text&gt; 4. repulsive force in all cases&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_checkpoint_w10_31_3_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_checkpoint_w10_31_3_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_checkpoint_w10_31_solution_2&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Forces on Moving Magnet&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_checkpoint_w10_31&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_checkpoint_w10_31&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;checkpoint_w10_31-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;checkpoint_w10_31-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;checkpoint_w10_31-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> </div> </div>