<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@vertical+block@vert-pset7.2" data-has-score="False" data-runtime-class="LmsRuntime" data-graded="False" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="vertical" data-runtime-version="1" data-request-token="875566ee2a2f11f0874b12f8c5a42579" data-init="VerticalStudentView"> <h2 class="hd hd-2 unit-title">Ampere&#39;s Law for a Coaxial Cable</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pset7_2"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pset7_2" data-has-score="True" data-runtime-class="LmsRuntime" data-graded="False" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="problem" data-runtime-version="1" data-request-token="875566ee2a2f11f0874b12f8c5a42579" data-init="XBlockToXModuleShim"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_pset7_2" class="problems-wrapper" role="group" aria-labelledby="pset7_2-problem-title" data-problem-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pset7_2" data-url="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@problem+block@pset7_2/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;pset7_2-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.2x+2T2018+type@problem+block@pset7_2-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Ampere&amp;#39;s Law for a Coaxial Cable &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.2x+2T2018+type@problem+block@pset7_2-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; A long coaxial cable consists of two concentric conductors. The inner conductor is a cylinder with radius [mathjaxinline]R_1[/mathjaxinline], and it carries a current [mathjaxinline]I[/mathjaxinline] uniformly distributed over its cross section. The outer conductor is a cylindrical shell with inner radius [mathjaxinline]R_2[/mathjaxinline] and outer radius [mathjaxinline]R_3[/mathjaxinline]. It carries a current [mathjaxinline]I[/mathjaxinline] that is also uniformly distributed over its cross section, and that is opposite in direction to the current of the inner conductor. Calculate the magnetic field [mathjaxinline]\vec{\textbf{B}}[/mathjaxinline] as a function of the distance [mathjaxinline]r[/mathjaxinline] from the axis. Use the coordinate system described in the figure below. &lt;/p&gt; &lt;p&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/2be086b1562d4dc1796272e6d533fdcc/asset-v1:MITx+8.02.2x+2T2018+type@asset+block/images_ps5_p1_fig0.png&#34; width=&#34;400&#34; style=&#34;width : 3.5in&#34;/&gt; &lt;/center&gt; &lt;/p&gt; &lt;p&gt; &lt;h2&gt;Symbolic Check&lt;/h2&gt; &lt;/p&gt; &lt;p&gt; For the symbolic check, write your answer using some or all of the following: [mathjaxinline]r[/mathjaxinline], [mathjaxinline]I[/mathjaxinline], R_1 for [mathjaxinline]R_1[/mathjaxinline], R_2 for [mathjaxinline]R_2[/mathjaxinline], R_3 for [mathjaxinline]R_3[/mathjaxinline] and mu_0 for [mathjaxinline]\mu _0[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;For [mathjaxinline]0 &amp;lt; r &amp;lt; R_1[/mathjaxinline]: [mathjaxinline]B(r) =[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_pset7_2_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_pset7_2_2_1&#34; id=&#34;input_pset7_2_2_1&#34; aria-describedby=&#34;status_pset7_2_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_pset7_2_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_pset7_2_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;p id=&#34;answer_pset7_2_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_pset7_2_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_pset7_2_2_1_dynamath&#34; name=&#34;input_pset7_2_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;Direction: &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 2&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;inputtype option-input inline&#34;&gt; &lt;select name=&#34;input_pset7_2_3_1&#34; id=&#34;input_pset7_2_3_1&#34; aria-describedby=&#34;status_pset7_2_3_1&#34;&gt; &lt;option value=&#34;option_pset7_2_3_1_dummy_default&#34;&gt;Select an option&lt;/option&gt; &lt;option value=&#34;[mathjaxinline]\hat r[/mathjaxinline]&#34;&gt; [mathjaxinline]\hat r[/mathjaxinline]&lt;/option&gt; &lt;option value=&#34;[mathjaxinline]-\hat r[/mathjaxinline]&#34;&gt; [mathjaxinline]-\hat r[/mathjaxinline]&lt;/option&gt; &lt;option value=&#34;[mathjaxinline]\hat\varphi[/mathjaxinline]&#34;&gt; [mathjaxinline]\hat\varphi[/mathjaxinline]&lt;/option&gt; &lt;option value=&#34;-[mathjaxinline]\hat\varphi[/mathjaxinline]&#34;&gt; -[mathjaxinline]\hat\varphi[/mathjaxinline]&lt;/option&gt; &lt;option value=&#34;[mathjaxinline]\hat z[/mathjaxinline]&#34;&gt; [mathjaxinline]\hat z[/mathjaxinline]&lt;/option&gt; &lt;option value=&#34;[mathjaxinline]-\hat z[/mathjaxinline]&#34;&gt; [mathjaxinline]-\hat z[/mathjaxinline]&lt;/option&gt; &lt;option value=&#34;None, B is zero&#34;&gt; None, B is zero&lt;/option&gt; &lt;/select&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_pset7_2_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;p class=&#34;answer&#34; id=&#34;answer_pset7_2_3_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p style=&#34;margin-bottom: 0px; margin-top: 0px; display: block; padding-bottom: 20px;&#34; class=&#34;gap&#34;/&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;For [mathjaxinline]R_1 &amp;lt; r &amp;lt; R_2[/mathjaxinline]: [mathjaxinline]B(r) =[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 3&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_pset7_2_4_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_pset7_2_4_1&#34; id=&#34;input_pset7_2_4_1&#34; aria-describedby=&#34;status_pset7_2_4_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_pset7_2_4_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_pset7_2_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;p id=&#34;answer_pset7_2_4_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_pset7_2_4_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_pset7_2_4_1_dynamath&#34; name=&#34;input_pset7_2_4_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;Direction: &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 4&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;inputtype option-input inline&#34;&gt; &lt;select name=&#34;input_pset7_2_5_1&#34; id=&#34;input_pset7_2_5_1&#34; aria-describedby=&#34;status_pset7_2_5_1&#34;&gt; &lt;option value=&#34;option_pset7_2_5_1_dummy_default&#34;&gt;Select an option&lt;/option&gt; &lt;option value=&#34;[mathjaxinline]\hat r[/mathjaxinline]&#34;&gt; [mathjaxinline]\hat r[/mathjaxinline]&lt;/option&gt; &lt;option value=&#34;[mathjaxinline]-\hat r[/mathjaxinline]&#34;&gt; [mathjaxinline]-\hat r[/mathjaxinline]&lt;/option&gt; &lt;option value=&#34;[mathjaxinline]\hat\varphi[/mathjaxinline]&#34;&gt; [mathjaxinline]\hat\varphi[/mathjaxinline]&lt;/option&gt; &lt;option value=&#34;-[mathjaxinline]\hat\varphi[/mathjaxinline]&#34;&gt; -[mathjaxinline]\hat\varphi[/mathjaxinline]&lt;/option&gt; &lt;option value=&#34;[mathjaxinline]\hat z[/mathjaxinline]&#34;&gt; [mathjaxinline]\hat z[/mathjaxinline]&lt;/option&gt; &lt;option value=&#34;[mathjaxinline]-\hat z[/mathjaxinline]&#34;&gt; [mathjaxinline]-\hat z[/mathjaxinline]&lt;/option&gt; &lt;option value=&#34;None, B is zero&#34;&gt; None, B is zero&lt;/option&gt; &lt;/select&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_pset7_2_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;p class=&#34;answer&#34; id=&#34;answer_pset7_2_5_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p style=&#34;margin-bottom: 0px; margin-top: 0px; display: block; padding-bottom: 20px;&#34; class=&#34;gap&#34;/&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;For [mathjaxinline]R_2 &amp;lt; r &amp;lt; R_3[/mathjaxinline]: [mathjaxinline]B(r) =[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 5&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_pset7_2_6_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_pset7_2_6_1&#34; id=&#34;input_pset7_2_6_1&#34; aria-describedby=&#34;status_pset7_2_6_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_pset7_2_6_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_pset7_2_6_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;p id=&#34;answer_pset7_2_6_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_pset7_2_6_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_pset7_2_6_1_dynamath&#34; name=&#34;input_pset7_2_6_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;Direction: &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 6&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;inputtype option-input inline&#34;&gt; &lt;select name=&#34;input_pset7_2_7_1&#34; id=&#34;input_pset7_2_7_1&#34; aria-describedby=&#34;status_pset7_2_7_1&#34;&gt; &lt;option value=&#34;option_pset7_2_7_1_dummy_default&#34;&gt;Select an option&lt;/option&gt; &lt;option value=&#34;[mathjaxinline]\hat r[/mathjaxinline]&#34;&gt; [mathjaxinline]\hat r[/mathjaxinline]&lt;/option&gt; &lt;option value=&#34;[mathjaxinline]-\hat r[/mathjaxinline]&#34;&gt; [mathjaxinline]-\hat r[/mathjaxinline]&lt;/option&gt; &lt;option value=&#34;[mathjaxinline]\hat\varphi[/mathjaxinline]&#34;&gt; [mathjaxinline]\hat\varphi[/mathjaxinline]&lt;/option&gt; &lt;option value=&#34;-[mathjaxinline]\hat\varphi[/mathjaxinline]&#34;&gt; -[mathjaxinline]\hat\varphi[/mathjaxinline]&lt;/option&gt; &lt;option value=&#34;[mathjaxinline]\hat z[/mathjaxinline]&#34;&gt; [mathjaxinline]\hat z[/mathjaxinline]&lt;/option&gt; &lt;option value=&#34;[mathjaxinline]-\hat z[/mathjaxinline]&#34;&gt; [mathjaxinline]-\hat z[/mathjaxinline]&lt;/option&gt; &lt;option value=&#34;None, B is zero&#34;&gt; None, B is zero&lt;/option&gt; &lt;/select&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_pset7_2_7_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;p class=&#34;answer&#34; id=&#34;answer_pset7_2_7_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p style=&#34;margin-bottom: 0px; margin-top: 0px; display: block; padding-bottom: 20px;&#34; class=&#34;gap&#34;/&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;For [mathjaxinline]R_3 &amp;lt; r[/mathjaxinline]: [mathjaxinline]B(r) =[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 7&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_pset7_2_8_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_pset7_2_8_1&#34; id=&#34;input_pset7_2_8_1&#34; aria-describedby=&#34;status_pset7_2_8_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_pset7_2_8_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_pset7_2_8_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;p id=&#34;answer_pset7_2_8_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_pset7_2_8_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_pset7_2_8_1_dynamath&#34; name=&#34;input_pset7_2_8_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;Direction: &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 8&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;inputtype option-input inline&#34;&gt; &lt;select name=&#34;input_pset7_2_9_1&#34; id=&#34;input_pset7_2_9_1&#34; aria-describedby=&#34;status_pset7_2_9_1&#34;&gt; &lt;option value=&#34;option_pset7_2_9_1_dummy_default&#34;&gt;Select an option&lt;/option&gt; &lt;option value=&#34;[mathjaxinline]\hat r[/mathjaxinline]&#34;&gt; [mathjaxinline]\hat r[/mathjaxinline]&lt;/option&gt; &lt;option value=&#34;[mathjaxinline]-\hat r[/mathjaxinline]&#34;&gt; [mathjaxinline]-\hat r[/mathjaxinline]&lt;/option&gt; &lt;option value=&#34;[mathjaxinline]\hat\varphi[/mathjaxinline]&#34;&gt; [mathjaxinline]\hat\varphi[/mathjaxinline]&lt;/option&gt; &lt;option value=&#34;-[mathjaxinline]\hat\varphi[/mathjaxinline]&#34;&gt; -[mathjaxinline]\hat\varphi[/mathjaxinline]&lt;/option&gt; &lt;option value=&#34;[mathjaxinline]\hat z[/mathjaxinline]&#34;&gt; [mathjaxinline]\hat z[/mathjaxinline]&lt;/option&gt; &lt;option value=&#34;[mathjaxinline]-\hat z[/mathjaxinline]&#34;&gt; [mathjaxinline]-\hat z[/mathjaxinline]&lt;/option&gt; &lt;option value=&#34;None, B is zero&#34;&gt; None, B is zero&lt;/option&gt; &lt;/select&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_pset7_2_9_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;p class=&#34;answer&#34; id=&#34;answer_pset7_2_9_1&#34;/&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_pset7_2_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;Ampere&amp;#39;s Law for a Coaxial Cable&#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_pset7_2&#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_pset7_2&#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;pset7_2-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;pset7_2-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;pset7_2-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="False"> <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 class="vert vert-1" data-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS03"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS03" data-has-score="False" data-runtime-class="LmsRuntime" data-graded="False" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="video" data-runtime-version="1" data-request-token="875566ee2a2f11f0874b12f8c5a42579" data-init="XBlockToXModuleShim"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Video"} </script> <h3 class="hd hd-2">W09PS03: Co-axial Cable</h3> <div id="video_W09PS03" class="video closed" data-metadata='{&#34;ytMetadataEndpoint&#34;: &#34;&#34;, &#34;transcriptAvailableTranslationsUrl&#34;: &#34;/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS03/handler/transcript/available_translations&#34;, &#34;sources&#34;: [], &#34;ytApiUrl&#34;: &#34;https://www.youtube.com/iframe_api&#34;, &#34;transcriptTranslationUrl&#34;: &#34;/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS03/handler/transcript/translation/__lang__&#34;, &#34;completionPercentage&#34;: 0.95, &#34;saveStateEnabled&#34;: false, &#34;prioritizeHls&#34;: false, &#34;speed&#34;: null, &#34;poster&#34;: null, &#34;captionDataDir&#34;: null, &#34;lmsRootURL&#34;: &#34;https://openlearninglibrary.mit.edu&#34;, &#34;showCaptions&#34;: &#34;true&#34;, &#34;recordedYoutubeIsAvailable&#34;: true, &#34;savedVideoPosition&#34;: 0.0, &#34;duration&#34;: null, &#34;completionEnabled&#34;: false, &#34;end&#34;: 0.0, &#34;autohideHtml5&#34;: false, &#34;start&#34;: 0.0, &#34;streams&#34;: &#34;1.00:-E6uMBntVqo&#34;, &#34;ytTestTimeout&#34;: 1500, &#34;transcriptLanguage&#34;: &#34;en&#34;, &#34;publishCompletionUrl&#34;: &#34;/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS03/handler/publish_completion&#34;, &#34;generalSpeed&#34;: 1.0, &#34;transcriptLanguages&#34;: {&#34;en&#34;: &#34;English&#34;}, &#34;autoplay&#34;: false, &#34;saveStateUrl&#34;: &#34;/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS03/handler/xmodule_handler/save_user_state&#34;, &#34;autoAdvance&#34;: false}' 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="W09PS03"></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_W09PS03">Downloads and transcripts</h3> <div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_W09PS03"> <div class="wrapper-download-transcripts"> <h4 class="hd hd-5">Transcripts</h4> <ul class="list-download-transcripts"> <li class="transcript-option"> <a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS03/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a> </li> <li class="transcript-option"> <a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS03/handler/transcript/download" data-value="txt">Download Text (.txt) file</a> </li> </ul> </div> </div> </div> </div> </div> </div> </div>

<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@vertical+block@vert-B-2slabs-superposition" data-has-score="False" data-runtime-class="LmsRuntime" data-graded="False" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="vertical" data-runtime-version="1" data-request-token="875566ee2a2f11f0874b12f8c5a42579" data-init="VerticalStudentView"> <h2 class="hd hd-2 unit-title">B-field of two Infinite Slabs - Superposition Principle to Obtain B-direction</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@fps_fridayw7_2"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@fps_fridayw7_2" data-has-score="True" data-runtime-class="LmsRuntime" data-graded="False" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="problem" data-runtime-version="1" data-request-token="875566ee2a2f11f0874b12f8c5a42579" data-init="XBlockToXModuleShim"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_fps_fridayw7_2" class="problems-wrapper" role="group" aria-labelledby="fps_fridayw7_2-problem-title" data-problem-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@fps_fridayw7_2" data-url="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@problem+block@fps_fridayw7_2/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;fps_fridayw7_2-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.2x+2T2018+type@problem+block@fps_fridayw7_2-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Current Slabs &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.2x+2T2018+type@problem+block@fps_fridayw7_2-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; The figure below shows two slabs of current. Both slabs are infinite in the [mathjaxinline]x[/mathjaxinline] and [mathjaxinline]z[/mathjaxinline] directions, and have thickness [mathjaxinline]d[/mathjaxinline] in the [mathjaxinline]y[/mathjaxinline] direction. The top slab of current is located in the region [mathjaxinline]0&amp;lt;y&amp;lt;d[/mathjaxinline] and has a constant current density [mathjaxinline]\vec{\mathbf{J}}_{out}=J \hat{\mathbf{z}}[/mathjaxinline], directed out of the screen as shown in the figure below. The bottom slab is located in the region [mathjaxinline]-d&amp;lt;y&amp;lt;0[/mathjaxinline] and has a constant current density [mathjaxinline]\vec{\mathbf{J}}_{in}=-J \hat{\mathbf{z}}[/mathjaxinline], directed into the screen. Note that the two slabs have current densities with the same magnitude but opposite directions so there is a discontinuity in the current density at [mathjaxinline]y=0[/mathjaxinline]. &lt;/p&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/1638a66738e02dd93abd8d10243f50b6/asset-v1:MITx+8.02.2x+2T2018+type@asset+block/images_fridayw7_2_fig1.png&#34; width=&#34;330&#34;/&gt; &lt;/center&gt; &lt;p&gt; For the following questions, express your answers in terms of mu_0 for [mathjaxinline]\mu _0[/mathjaxinline], [mathjaxinline]J[/mathjaxinline], [mathjaxinline]d[/mathjaxinline], [mathjaxinline]y[/mathjaxinline], hati for [mathjaxinline]\hat{i}[/mathjaxinline], hatj for [mathjaxinline]\hat{j}[/mathjaxinline], and hatk for [mathjaxinline]\hat{k}[/mathjaxinline] (where [mathjaxinline]\hat{i}[/mathjaxinline], [mathjaxinline]\hat{j}[/mathjaxinline], and [mathjaxinline]\hat{k}[/mathjaxinline] point in the [mathjaxinline]x[/mathjaxinline], [mathjaxinline]y[/mathjaxinline], and [mathjaxinline]z[/mathjaxinline] directions, respectively), as needed. &lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(a)&lt;/b&gt; What is the direction and magnitude of the magnetic field for [mathjaxinline]|y|&amp;gt;d[/mathjaxinline]? &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]\vec{\mathbf{B}}=[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_fps_fridayw7_2_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_fps_fridayw7_2_2_1&#34; id=&#34;input_fps_fridayw7_2_2_1&#34; aria-describedby=&#34;status_fps_fridayw7_2_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;40&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_fps_fridayw7_2_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_fps_fridayw7_2_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;p id=&#34;answer_fps_fridayw7_2_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_fps_fridayw7_2_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_fps_fridayw7_2_2_1_dynamath&#34; name=&#34;input_fps_fridayw7_2_2_1_dynamath&#34;/&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_fps_fridayw7_2_solution_1&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(b)&lt;/b&gt; Use Ampere&#39;s Law to find the direction and magnitude of the magnetic field at [mathjaxinline]y=0[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]\vec{\mathbf{B}}=[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 2&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_fps_fridayw7_2_3_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_fps_fridayw7_2_3_1&#34; id=&#34;input_fps_fridayw7_2_3_1&#34; aria-describedby=&#34;status_fps_fridayw7_2_3_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;40&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_fps_fridayw7_2_3_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_fps_fridayw7_2_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;p id=&#34;answer_fps_fridayw7_2_3_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_fps_fridayw7_2_3_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_fps_fridayw7_2_3_1_dynamath&#34; name=&#34;input_fps_fridayw7_2_3_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(c)&lt;/b&gt; Use Ampere&#39;s Law to find the direction and magnitude of the magnetic field for [mathjaxinline]0&amp;lt;y&amp;lt;d[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]\vec{\mathbf{B}}=[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 3&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_fps_fridayw7_2_4_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_fps_fridayw7_2_4_1&#34; id=&#34;input_fps_fridayw7_2_4_1&#34; aria-describedby=&#34;status_fps_fridayw7_2_4_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;40&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_fps_fridayw7_2_4_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_fps_fridayw7_2_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;p id=&#34;answer_fps_fridayw7_2_4_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_fps_fridayw7_2_4_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_fps_fridayw7_2_4_1_dynamath&#34; name=&#34;input_fps_fridayw7_2_4_1_dynamath&#34;/&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_fps_fridayw7_2_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;Current Slabs&#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_fps_fridayw7_2&#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_fps_fridayw7_2&#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;fps_fridayw7_2-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;fps_fridayw7_2-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;fps_fridayw7_2-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="False"> <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 class="vert vert-1" data-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS01a"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS01a" data-has-score="False" data-runtime-class="LmsRuntime" data-graded="False" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="video" data-runtime-version="1" data-request-token="875566ee2a2f11f0874b12f8c5a42579" data-init="XBlockToXModuleShim"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Video"} </script> <h3 class="hd hd-2">W09PS01a: Two Infinite Slabs of Current - Shape of the Magnetic Field</h3> <div id="video_W09PS01a" class="video closed" data-metadata='{&#34;ytMetadataEndpoint&#34;: &#34;&#34;, &#34;transcriptAvailableTranslationsUrl&#34;: &#34;/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS01a/handler/transcript/available_translations&#34;, &#34;sources&#34;: [], &#34;ytApiUrl&#34;: &#34;https://www.youtube.com/iframe_api&#34;, &#34;transcriptTranslationUrl&#34;: &#34;/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS01a/handler/transcript/translation/__lang__&#34;, &#34;completionPercentage&#34;: 0.95, &#34;saveStateEnabled&#34;: false, &#34;prioritizeHls&#34;: false, &#34;speed&#34;: null, &#34;poster&#34;: null, &#34;captionDataDir&#34;: null, &#34;lmsRootURL&#34;: &#34;https://openlearninglibrary.mit.edu&#34;, &#34;showCaptions&#34;: &#34;true&#34;, &#34;recordedYoutubeIsAvailable&#34;: true, &#34;savedVideoPosition&#34;: 0.0, &#34;duration&#34;: null, &#34;completionEnabled&#34;: false, &#34;end&#34;: 0.0, &#34;autohideHtml5&#34;: false, &#34;start&#34;: 0.0, &#34;streams&#34;: &#34;1.00:8YQa6WYhCBE&#34;, &#34;ytTestTimeout&#34;: 1500, &#34;transcriptLanguage&#34;: &#34;en&#34;, &#34;publishCompletionUrl&#34;: &#34;/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS01a/handler/publish_completion&#34;, &#34;generalSpeed&#34;: 1.0, &#34;transcriptLanguages&#34;: {&#34;en&#34;: &#34;English&#34;}, &#34;autoplay&#34;: false, &#34;saveStateUrl&#34;: &#34;/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS01a/handler/xmodule_handler/save_user_state&#34;, &#34;autoAdvance&#34;: false}' 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="W09PS01a"></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_W09PS01a">Downloads and transcripts</h3> <div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_W09PS01a"> <div class="wrapper-download-transcripts"> <h4 class="hd hd-5">Transcripts</h4> <ul class="list-download-transcripts"> <li class="transcript-option"> <a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS01a/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a> </li> <li class="transcript-option"> <a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS01a/handler/transcript/download" data-value="txt">Download Text (.txt) file</a> </li> </ul> </div> </div> </div> </div> </div> <div class="vert vert-2" data-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS01b"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS01b" data-has-score="False" data-runtime-class="LmsRuntime" data-graded="False" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="video" data-runtime-version="1" data-request-token="875566ee2a2f11f0874b12f8c5a42579" data-init="XBlockToXModuleShim"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Video"} </script> <h3 class="hd hd-2">W09PS01b: Two Infinite Slabs of Current - Solve for B Inside</h3> <div id="video_W09PS01b" class="video closed" data-metadata='{&#34;ytMetadataEndpoint&#34;: &#34;&#34;, &#34;transcriptAvailableTranslationsUrl&#34;: &#34;/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS01b/handler/transcript/available_translations&#34;, &#34;sources&#34;: [], &#34;ytApiUrl&#34;: &#34;https://www.youtube.com/iframe_api&#34;, &#34;transcriptTranslationUrl&#34;: &#34;/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS01b/handler/transcript/translation/__lang__&#34;, &#34;completionPercentage&#34;: 0.95, &#34;saveStateEnabled&#34;: false, &#34;prioritizeHls&#34;: false, &#34;speed&#34;: null, &#34;poster&#34;: null, &#34;captionDataDir&#34;: null, &#34;lmsRootURL&#34;: &#34;https://openlearninglibrary.mit.edu&#34;, &#34;showCaptions&#34;: &#34;true&#34;, &#34;recordedYoutubeIsAvailable&#34;: true, &#34;savedVideoPosition&#34;: 0.0, &#34;duration&#34;: null, &#34;completionEnabled&#34;: false, &#34;end&#34;: 0.0, &#34;autohideHtml5&#34;: false, &#34;start&#34;: 0.0, &#34;streams&#34;: &#34;1.00:kyCuTbbWgHY&#34;, &#34;ytTestTimeout&#34;: 1500, &#34;transcriptLanguage&#34;: &#34;en&#34;, &#34;publishCompletionUrl&#34;: &#34;/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS01b/handler/publish_completion&#34;, &#34;generalSpeed&#34;: 1.0, &#34;transcriptLanguages&#34;: {&#34;en&#34;: &#34;English&#34;}, &#34;autoplay&#34;: false, &#34;saveStateUrl&#34;: &#34;/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS01b/handler/xmodule_handler/save_user_state&#34;, &#34;autoAdvance&#34;: false}' 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="W09PS01b"></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_W09PS01b">Downloads and transcripts</h3> <div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_W09PS01b"> <div class="wrapper-download-transcripts"> <h4 class="hd hd-5">Transcripts</h4> <ul class="list-download-transcripts"> <li class="transcript-option"> <a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS01b/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a> </li> <li class="transcript-option"> <a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS01b/handler/transcript/download" data-value="txt">Download Text (.txt) file</a> </li> </ul> </div> </div> </div> </div> </div> <div class="vert vert-3" data-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS01c"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS01c" data-has-score="False" data-runtime-class="LmsRuntime" data-graded="False" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="video" data-runtime-version="1" data-request-token="875566ee2a2f11f0874b12f8c5a42579" data-init="XBlockToXModuleShim"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Video"} </script> <h3 class="hd hd-2">W09PS01c: Two Infinite Slabs of Current - Another Choice of Loop</h3> <div id="video_W09PS01c" class="video closed" data-metadata='{&#34;ytMetadataEndpoint&#34;: &#34;&#34;, &#34;transcriptAvailableTranslationsUrl&#34;: &#34;/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS01c/handler/transcript/available_translations&#34;, &#34;sources&#34;: [], &#34;ytApiUrl&#34;: &#34;https://www.youtube.com/iframe_api&#34;, &#34;transcriptTranslationUrl&#34;: &#34;/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS01c/handler/transcript/translation/__lang__&#34;, &#34;completionPercentage&#34;: 0.95, &#34;saveStateEnabled&#34;: false, &#34;prioritizeHls&#34;: false, &#34;speed&#34;: null, &#34;poster&#34;: null, &#34;captionDataDir&#34;: null, &#34;lmsRootURL&#34;: &#34;https://openlearninglibrary.mit.edu&#34;, &#34;showCaptions&#34;: &#34;true&#34;, &#34;recordedYoutubeIsAvailable&#34;: true, &#34;savedVideoPosition&#34;: 0.0, &#34;duration&#34;: null, &#34;completionEnabled&#34;: false, &#34;end&#34;: 0.0, &#34;autohideHtml5&#34;: false, &#34;start&#34;: 0.0, &#34;streams&#34;: &#34;1.00:mmbXI2uDRZ0&#34;, &#34;ytTestTimeout&#34;: 1500, &#34;transcriptLanguage&#34;: &#34;en&#34;, &#34;publishCompletionUrl&#34;: &#34;/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS01c/handler/publish_completion&#34;, &#34;generalSpeed&#34;: 1.0, &#34;transcriptLanguages&#34;: {&#34;en&#34;: &#34;English&#34;}, &#34;autoplay&#34;: false, &#34;saveStateUrl&#34;: &#34;/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS01c/handler/xmodule_handler/save_user_state&#34;, &#34;autoAdvance&#34;: false}' 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="W09PS01c"></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_W09PS01c">Downloads and transcripts</h3> <div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_W09PS01c"> <div class="wrapper-download-transcripts"> <h4 class="hd hd-5">Transcripts</h4> <ul class="list-download-transcripts"> <li class="transcript-option"> <a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS01c/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a> </li> <li class="transcript-option"> <a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS01c/handler/transcript/download" data-value="txt">Download Text (.txt) file</a> </li> </ul> </div> </div> </div> </div> </div> </div> </div>

<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@vertical+block@vert-w7d3p3" data-has-score="False" data-runtime-class="LmsRuntime" data-graded="False" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="vertical" data-runtime-version="1" data-request-token="875566ee2a2f11f0874b12f8c5a42579" data-init="VerticalStudentView"> <h2 class="hd hd-2 unit-title">Magnetic Field of a Non-Uniform Slab of Current</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@fps_fridayw7_3"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@fps_fridayw7_3" data-has-score="True" data-runtime-class="LmsRuntime" data-graded="False" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="problem" data-runtime-version="1" data-request-token="875566ee2a2f11f0874b12f8c5a42579" data-init="XBlockToXModuleShim"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_fps_fridayw7_3" class="problems-wrapper" role="group" aria-labelledby="fps_fridayw7_3-problem-title" data-problem-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@fps_fridayw7_3" data-url="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@problem+block@fps_fridayw7_3/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;fps_fridayw7_3-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.2x+2T2018+type@problem+block@fps_fridayw7_3-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Magnetic Field of a Non-uniform Slab of Current &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.2x+2T2018+type@problem+block@fps_fridayw7_3-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; We want to find the magnetic field [mathjaxinline]\vec{\mathbf{B}}[/mathjaxinline] due to an infinite slab of current, using Ampere&#39;s Law. The figure shows a slab of current with non-uniform current density [mathjaxinline]\vec{\mathbf{J}}=(2J_ e |y|/d)\hat{\mathbf{z}}[/mathjaxinline], where [mathjaxinline]J_ e[/mathjaxinline] is a positive constant with units of amps per square meter and [mathjaxinline]\hat{\mathbf{z}}[/mathjaxinline] points out of the screen. Note the absolute value [mathjaxinline]|y|[/mathjaxinline] in the expression for the current density, which means that the current density always points out of the screen. The slab of current is infinite in the [mathjaxinline]x[/mathjaxinline] and [mathjaxinline]z[/mathjaxinline] directions, and has thickness [mathjaxinline]d[/mathjaxinline] in the [mathjaxinline]y[/mathjaxinline] direction. Find expressions for the direction and magnitude of the magnetic field as a function of [mathjaxinline]y[/mathjaxinline] in the regions listed below. &lt;/p&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/504ba9c6053fe3b1a374b366226a9108/asset-v1:MITx+8.02.2x+2T2018+type@asset+block/images_fridayw7_3_fig1.png&#34; width=&#34;550&#34;/&gt; &lt;/center&gt; &lt;p&gt; Express your answers for [mathjaxinline]\vec{\mathbf{B}}[/mathjaxinline], in terms of mu_0 for [mathjaxinline]\mu _0[/mathjaxinline], J_e for [mathjaxinline]J_ e[/mathjaxinline], [mathjaxinline]d[/mathjaxinline], [mathjaxinline]y[/mathjaxinline], hati for [mathjaxinline]\hat{i}[/mathjaxinline], hatj for [mathjaxinline]\hat{j}[/mathjaxinline], and hatk for [mathjaxinline]\hat{k}[/mathjaxinline] (where [mathjaxinline]\hat{i}[/mathjaxinline], [mathjaxinline]\hat{j}[/mathjaxinline], [mathjaxinline]\hat{k}[/mathjaxinline] point along the [mathjaxinline]x[/mathjaxinline], [mathjaxinline]y[/mathjaxinline], and [mathjaxinline]z[/mathjaxinline] directions, respectively), as needed. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;For [mathjaxinline]y\leqslant -d/2[/mathjaxinline] (below the slab), [mathjaxinline]\vec{\mathbf{B}}=[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_fps_fridayw7_3_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_fps_fridayw7_3_2_1&#34; id=&#34;input_fps_fridayw7_3_2_1&#34; aria-describedby=&#34;status_fps_fridayw7_3_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;40&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_fps_fridayw7_3_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_fps_fridayw7_3_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;p id=&#34;answer_fps_fridayw7_3_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_fps_fridayw7_3_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_fps_fridayw7_3_2_1_dynamath&#34; name=&#34;input_fps_fridayw7_3_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;For [mathjaxinline]-d/2 \leqslant y\leqslant 0[/mathjaxinline] (in the lower half of the slab), [mathjaxinline]\vec{\mathbf{B}}=[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 2&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_fps_fridayw7_3_3_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_fps_fridayw7_3_3_1&#34; id=&#34;input_fps_fridayw7_3_3_1&#34; aria-describedby=&#34;status_fps_fridayw7_3_3_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;40&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_fps_fridayw7_3_3_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_fps_fridayw7_3_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;p id=&#34;answer_fps_fridayw7_3_3_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_fps_fridayw7_3_3_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_fps_fridayw7_3_3_1_dynamath&#34; name=&#34;input_fps_fridayw7_3_3_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;For [mathjaxinline]0 \leqslant y\leqslant d/2[/mathjaxinline] (in the upper half of the slab), [mathjaxinline]\vec{\mathbf{B}}=[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 3&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_fps_fridayw7_3_4_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_fps_fridayw7_3_4_1&#34; id=&#34;input_fps_fridayw7_3_4_1&#34; aria-describedby=&#34;status_fps_fridayw7_3_4_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;40&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_fps_fridayw7_3_4_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_fps_fridayw7_3_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;p id=&#34;answer_fps_fridayw7_3_4_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_fps_fridayw7_3_4_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_fps_fridayw7_3_4_1_dynamath&#34; name=&#34;input_fps_fridayw7_3_4_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;For [mathjaxinline]y\geqslant d/2[/mathjaxinline] (above the slab), [mathjaxinline]\vec{\mathbf{B}}=[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 4&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_fps_fridayw7_3_5_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_fps_fridayw7_3_5_1&#34; id=&#34;input_fps_fridayw7_3_5_1&#34; aria-describedby=&#34;status_fps_fridayw7_3_5_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;40&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_fps_fridayw7_3_5_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_fps_fridayw7_3_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;p id=&#34;answer_fps_fridayw7_3_5_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_fps_fridayw7_3_5_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_fps_fridayw7_3_5_1_dynamath&#34; name=&#34;input_fps_fridayw7_3_5_1_dynamath&#34;/&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_fps_fridayw7_3_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;Magnetic Field of a Non-uniform Slab of Current&#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_fps_fridayw7_3&#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_fps_fridayw7_3&#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;fps_fridayw7_3-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;fps_fridayw7_3-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;fps_fridayw7_3-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="False"> <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 class="vert vert-1" data-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS02"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS02" data-has-score="False" data-runtime-class="LmsRuntime" data-graded="False" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="video" data-runtime-version="1" data-request-token="875566ee2a2f11f0874b12f8c5a42579" data-init="XBlockToXModuleShim"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Video"} </script> <h3 class="hd hd-2">W09PS02: Non-Uniform Slab of Current</h3> <div id="video_W09PS02" class="video closed" data-metadata='{&#34;ytMetadataEndpoint&#34;: &#34;&#34;, &#34;transcriptAvailableTranslationsUrl&#34;: &#34;/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS02/handler/transcript/available_translations&#34;, &#34;sources&#34;: [], &#34;ytApiUrl&#34;: &#34;https://www.youtube.com/iframe_api&#34;, &#34;transcriptTranslationUrl&#34;: &#34;/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS02/handler/transcript/translation/__lang__&#34;, &#34;completionPercentage&#34;: 0.95, &#34;saveStateEnabled&#34;: false, &#34;prioritizeHls&#34;: false, &#34;speed&#34;: null, &#34;poster&#34;: null, &#34;captionDataDir&#34;: null, &#34;lmsRootURL&#34;: &#34;https://openlearninglibrary.mit.edu&#34;, &#34;showCaptions&#34;: &#34;true&#34;, &#34;recordedYoutubeIsAvailable&#34;: true, &#34;savedVideoPosition&#34;: 0.0, &#34;duration&#34;: null, &#34;completionEnabled&#34;: false, &#34;end&#34;: 0.0, &#34;autohideHtml5&#34;: false, &#34;start&#34;: 0.0, &#34;streams&#34;: &#34;1.00:An5b5lgvjgs&#34;, &#34;ytTestTimeout&#34;: 1500, &#34;transcriptLanguage&#34;: &#34;en&#34;, &#34;publishCompletionUrl&#34;: &#34;/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS02/handler/publish_completion&#34;, &#34;generalSpeed&#34;: 1.0, &#34;transcriptLanguages&#34;: {&#34;en&#34;: &#34;English&#34;}, &#34;autoplay&#34;: false, &#34;saveStateUrl&#34;: &#34;/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS02/handler/xmodule_handler/save_user_state&#34;, &#34;autoAdvance&#34;: false}' 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="W09PS02"></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_W09PS02">Downloads and transcripts</h3> <div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_W09PS02"> <div class="wrapper-download-transcripts"> <h4 class="hd hd-5">Transcripts</h4> <ul class="list-download-transcripts"> <li class="transcript-option"> <a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS02/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a> </li> <li class="transcript-option"> <a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@W09PS02/handler/transcript/download" data-value="txt">Download Text (.txt) file</a> </li> </ul> </div> </div> </div> </div> </div> </div> </div>

<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@vertical+block@vert-pset7.3" data-has-score="False" data-runtime-class="LmsRuntime" data-graded="False" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="vertical" data-runtime-version="1" data-request-token="875566ee2a2f11f0874b12f8c5a42579" data-init="VerticalStudentView"> <h2 class="hd hd-2 unit-title">Magnetic Field of a Toroid</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pset7_3"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pset7_3" data-has-score="True" data-runtime-class="LmsRuntime" data-graded="False" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="problem" data-runtime-version="1" data-request-token="875566ee2a2f11f0874b12f8c5a42579" data-init="XBlockToXModuleShim"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_pset7_3" class="problems-wrapper" role="group" aria-labelledby="pset7_3-problem-title" data-problem-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pset7_3" data-url="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@problem+block@pset7_3/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;pset7_3-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.2x+2T2018+type@problem+block@pset7_3-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Magnetic Field of a Toroid &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.2x+2T2018+type@problem+block@pset7_3-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; A toroid has [mathjaxinline]N[/mathjaxinline] turns, and an inner radius [mathjaxinline]a[/mathjaxinline], outer radius [mathjaxinline]b[/mathjaxinline], and height [mathjaxinline]h[/mathjaxinline]. The toroid has a rectangular cross section shown in the figures below. &lt;/p&gt; &lt;p&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/c163e1d10be5e39b614af89081b0fef3/asset-v1:MITx+8.02.2x+2T2018+type@asset+block/images_Spring_2014_pset7_3-fig005.jpg&#34; width=&#34;330&#34;/&gt; &lt;/center&gt; &lt;/p&gt; &lt;p&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/4ea60d4cc7a112687331e89f9a30f503/asset-v1:MITx+8.02.2x+2T2018+type@asset+block/images_Spring_2014_pset7_3-fig006.jpg&#34; width=&#34;330&#34;/&gt; &lt;/center&gt; &lt;/p&gt; &lt;p&gt; When a current [mathjaxinline]I[/mathjaxinline] is flowing through the toroid, what are the magnitude and direction of the magnetic field inside the toroid as a function of distance [mathjaxinline]r[/mathjaxinline] from the axis of the toroid? &lt;/p&gt; &lt;p&gt; Write your answers using some or all of the following: mu_0 for [mathjaxinline]\mu _0[/mathjaxinline], pi for [mathjaxinline]\pi[/mathjaxinline], [mathjaxinline]N[/mathjaxinline], [mathjaxinline]r[/mathjaxinline], [mathjaxinline]a[/mathjaxinline], [mathjaxinline]b[/mathjaxinline], and [mathjaxinline]I[/mathjaxinline]. Use hatr, hattheta and hatk for [mathjaxinline]\hat{\mathbf{r}}[/mathjaxinline] (unit vector radially out for the center of the toroid), [mathjaxinline]\hat{\mathbf{\theta }}[/mathjaxinline] (unit vector tangent to direction going around the toroid clockwise as viewed from above) and [mathjaxinline]\hat{\mathbf{k}}[/mathjaxinline] (unit vector in the vertical direction), respectively. As shown above, the current is moving in the [mathjaxinline]-\hat{\mathbf{r}}[/mathjaxinline] direction on the top, the [mathjaxinline]-\hat{\mathbf{k}}[/mathjaxinline] direction in the hole of the toroid, and in the positive radial and vertical directions on the other two sides. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]\vec{B}(r&amp;lt;a)=[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_pset7_3_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_pset7_3_2_1&#34; id=&#34;input_pset7_3_2_1&#34; aria-describedby=&#34;status_pset7_3_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;60&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_pset7_3_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_pset7_3_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;p id=&#34;answer_pset7_3_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_pset7_3_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_pset7_3_2_1_dynamath&#34; name=&#34;input_pset7_3_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p style=&#34;margin-bottom: 0px; margin-top: 0px; display: block; padding-bottom: 20px;&#34; class=&#34;gap&#34;/&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]\vec{B}(a&amp;lt;r&amp;lt;b) =[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 2&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_pset7_3_3_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_pset7_3_3_1&#34; id=&#34;input_pset7_3_3_1&#34; aria-describedby=&#34;status_pset7_3_3_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;60&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_pset7_3_3_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_pset7_3_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;p id=&#34;answer_pset7_3_3_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_pset7_3_3_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_pset7_3_3_1_dynamath&#34; name=&#34;input_pset7_3_3_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p style=&#34;margin-bottom: 0px; margin-top: 0px; display: block; padding-bottom: 20px;&#34; class=&#34;gap&#34;/&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]\vec{B} (r&amp;gt;b) =[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 3&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_pset7_3_4_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_pset7_3_4_1&#34; id=&#34;input_pset7_3_4_1&#34; aria-describedby=&#34;status_pset7_3_4_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;60&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_pset7_3_4_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_pset7_3_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;p id=&#34;answer_pset7_3_4_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_pset7_3_4_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_pset7_3_4_1_dynamath&#34; name=&#34;input_pset7_3_4_1_dynamath&#34;/&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_pset7_3_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;Magnetic Field of a Toroid&#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_pset7_3&#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_pset7_3&#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;pset7_3-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;pset7_3-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;pset7_3-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="False"> <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>