<div class="xblock xblock-public_view xblock-public_view-vertical" data-runtime-version="1" data-block-type="vertical" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="VerticalStudentView" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="False" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-lesson01-textbooklinks"> <h2 class="hd hd-2 unit-title">Textbook Links</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@html+block@html-lesson01-textbooklinks"> <div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-runtime-version="1" data-block-type="html" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="False" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@html+block@html-lesson01-textbooklinks"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "HTMLModule"} </script> <p> This first lesson introduces electric charge and the forces between electric charges.</p><p> Textbook Links </p><ul><li> Chapter 2: Coulomb's Law <a href="/courses/course-v1:MITx+8.02.1x+1T2019/pdfbook/0/chapter/2/3"><i class="it">chapter 2, sections 1-3</i></a></li></ul> </div> </div> </div> </div>

<div class="xblock xblock-public_view xblock-public_view-vertical" data-runtime-version="1" data-block-type="vertical" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="VerticalStudentView" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="False" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-L01v01"> <h2 class="hd hd-2 unit-title">L1v1: What is Charge</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v01"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-runtime-version="1" data-block-type="video" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="False" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v01"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Video"} </script> <h3 class="hd hd-2">L01v01: What is Charge</h3> <div id="video_L01v01" class="video closed" data-metadata='{&#34;showCaptions&#34;: &#34;true&#34;, &#34;speed&#34;: null, &#34;ytMetadataEndpoint&#34;: &#34;&#34;, &#34;recordedYoutubeIsAvailable&#34;: true, &#34;ytTestTimeout&#34;: 1500, &#34;duration&#34;: 0.0, &#34;generalSpeed&#34;: 1.0, &#34;lmsRootURL&#34;: &#34;https://openlearninglibrary.mit.edu&#34;, &#34;autoplay&#34;: false, &#34;transcriptTranslationUrl&#34;: &#34;/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v01/handler/transcript/translation/__lang__&#34;, &#34;transcriptAvailableTranslationsUrl&#34;: &#34;/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v01/handler/transcript/available_translations&#34;, &#34;transcriptLanguages&#34;: {&#34;en&#34;: &#34;English&#34;}, &#34;savedVideoPosition&#34;: 0.0, &#34;completionPercentage&#34;: 0.95, &#34;prioritizeHls&#34;: false, &#34;autohideHtml5&#34;: false, &#34;start&#34;: 0.0, &#34;poster&#34;: null, &#34;streams&#34;: &#34;1.00:bxufkxbOOyE&#34;, &#34;sources&#34;: [], &#34;saveStateEnabled&#34;: false, &#34;completionEnabled&#34;: false, &#34;saveStateUrl&#34;: &#34;/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v01/handler/xmodule_handler/save_user_state&#34;, &#34;autoAdvance&#34;: false, &#34;transcriptLanguage&#34;: &#34;en&#34;, &#34;publishCompletionUrl&#34;: &#34;/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v01/handler/publish_completion&#34;, &#34;captionDataDir&#34;: null, &#34;end&#34;: 0.0, &#34;ytApiUrl&#34;: &#34;https://www.youtube.com/iframe_api&#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="L01v01"></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_L01v01">Downloads and transcripts</h3> <div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L01v01"> <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+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v01/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+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v01/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-runtime-version="1" data-block-type="vertical" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="VerticalStudentView" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="False" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-l01Q01"> <h2 class="hd hd-2 unit-title">L1Q1: Electric Charge Properties. </h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w1d2a"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-runtime-version="1" data-block-type="problem" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="True" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w1d2a"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_pcq_w1d2a" class="problems-wrapper" role="group" aria-labelledby="pcq_w1d2a-problem-title" data-problem-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w1d2a" data-url="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w1d2a/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.5" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;pcq_w1d2a-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w1d2a-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Electric Charge &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w1d2a-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Which of the following statements about electric charge is (are) true?&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_pcq_w1d2a_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_pcq_w1d2a_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_pcq_w1d2a_2_1[]&#34; id=&#34;input_pcq_w1d2a_2_1_choice_0&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_0&#34;/&gt;&lt;label id=&#34;pcq_w1d2a_2_1-choice_0-label&#34; for=&#34;input_pcq_w1d2a_2_1_choice_0&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pcq_w1d2a_2_1&#34;&gt; &lt;text&gt;a) It is conserved&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_pcq_w1d2a_2_1[]&#34; id=&#34;input_pcq_w1d2a_2_1_choice_1&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;pcq_w1d2a_2_1-choice_1-label&#34; for=&#34;input_pcq_w1d2a_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pcq_w1d2a_2_1&#34;&gt; &lt;text&gt;b) Like kinds of electric charge attract; unlike repel each other&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_pcq_w1d2a_2_1[]&#34; id=&#34;input_pcq_w1d2a_2_1_choice_2&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;pcq_w1d2a_2_1-choice_2-label&#34; for=&#34;input_pcq_w1d2a_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pcq_w1d2a_2_1&#34;&gt; &lt;text&gt;c) Electric charge can be of arbitrarily small amounts&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_pcq_w1d2a_2_1[]&#34; id=&#34;input_pcq_w1d2a_2_1_choice_3&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;pcq_w1d2a_2_1-choice_3-label&#34; for=&#34;input_pcq_w1d2a_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pcq_w1d2a_2_1&#34;&gt; &lt;text&gt;d) There are two kinds, negative and positive&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_pcq_w1d2a_2_1[]&#34; id=&#34;input_pcq_w1d2a_2_1_choice_4&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_4&#34;/&gt;&lt;label id=&#34;pcq_w1d2a_2_1-choice_4-label&#34; 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&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 class="vert vert-1" data-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w1d2b"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-runtime-version="1" data-block-type="problem" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="True" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w1d2b"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_pcq_w1d2b" class="problems-wrapper" role="group" aria-labelledby="pcq_w1d2b-problem-title" data-problem-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w1d2b" data-url="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w1d2b/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;pcq_w1d2b-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w1d2b-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Charge is Conserved &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w1d2b-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;In the statement &#34;Electric charge is conserved&#34; what does &#34;conserved&#34; mean?&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_pcq_w1d2b_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_pcq_w1d2b_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_pcq_w1d2b_2_1&#34; id=&#34;input_pcq_w1d2b_2_1_choice_1&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;pcq_w1d2b_2_1-choice_1-label&#34; for=&#34;input_pcq_w1d2b_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pcq_w1d2b_2_1&#34;&gt; &lt;text&gt;a) A charged object will always remain charged.&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_pcq_w1d2b_2_1&#34; id=&#34;input_pcq_w1d2b_2_1_choice_2&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;pcq_w1d2b_2_1-choice_2-label&#34; for=&#34;input_pcq_w1d2b_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pcq_w1d2b_2_1&#34;&gt; &lt;text&gt;b) The sum of negative charges in the Universe does not change.&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_pcq_w1d2b_2_1&#34; id=&#34;input_pcq_w1d2b_2_1_choice_3&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;pcq_w1d2b_2_1-choice_3-label&#34; for=&#34;input_pcq_w1d2b_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pcq_w1d2b_2_1&#34;&gt; &lt;text&gt;c) The number of negative and positive charges in the Universe does not change.&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_pcq_w1d2b_2_1&#34; id=&#34;input_pcq_w1d2b_2_1_choice_4&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_4&#34;/&gt;&lt;label id=&#34;pcq_w1d2b_2_1-choice_4-label&#34; for=&#34;input_pcq_w1d2b_2_1_choice_4&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pcq_w1d2b_2_1&#34;&gt; &lt;text&gt;d) The total sum of the positive charges in the Universe does not change.&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_pcq_w1d2b_2_1&#34; id=&#34;input_pcq_w1d2b_2_1_choice_5&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_5&#34;/&gt;&lt;label id=&#34;pcq_w1d2b_2_1-choice_5-label&#34; for=&#34;input_pcq_w1d2b_2_1_choice_5&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pcq_w1d2b_2_1&#34;&gt; &lt;text&gt;e) The total sum of the negative and positive charge in the Universe does not change.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_pcq_w1d2b_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_pcq_w1d2b_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;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_pcq_w1d2b_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Charge is Conserved&#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_pcq_w1d2b&#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_pcq_w1d2b&#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;span class=&#34;problem-action-button-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;save problem-action-btn btn-default btn-small&#34; data-value=&#34;Save&#34;&gt; &lt;span class=&#34;icon fa fa-floppy-o&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span aria-hidden=&#34;true&#34;&gt;Save&lt;/span&gt; &lt;span class=&#34;sr&#34;&gt;Save your answer&lt;/span&gt; &lt;/button&gt; &lt;/span&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;pcq_w1d2b-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; 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&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 class="vert vert-2" data-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w1d2c"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-runtime-version="1" data-block-type="problem" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="True" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w1d2c"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_pcq_w1d2c" class="problems-wrapper" role="group" aria-labelledby="pcq_w1d2c-problem-title" data-problem-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w1d2c" data-url="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w1d2c/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;pcq_w1d2c-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w1d2c-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Charge is Quantized &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w1d2c-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;In the statement &#34;Electric charge is quantized&#34; what does &#34;quantized&#34; mean?&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_pcq_w1d2c_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_pcq_w1d2c_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_pcq_w1d2c_2_1&#34; id=&#34;input_pcq_w1d2c_2_1_choice_1&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;pcq_w1d2c_2_1-choice_1-label&#34; for=&#34;input_pcq_w1d2c_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pcq_w1d2c_2_1&#34;&gt; &lt;text&gt;a) A charged object has a definite quantity of charge.&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_pcq_w1d2c_2_1&#34; id=&#34;input_pcq_w1d2c_2_1_choice_2&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;pcq_w1d2c_2_1-choice_2-label&#34; for=&#34;input_pcq_w1d2c_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pcq_w1d2c_2_1&#34;&gt; &lt;text&gt;b) The charge on an object can be measured in quants.&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_pcq_w1d2c_2_1&#34; id=&#34;input_pcq_w1d2c_2_1_choice_3&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;pcq_w1d2c_2_1-choice_3-label&#34; for=&#34;input_pcq_w1d2c_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pcq_w1d2c_2_1&#34;&gt; &lt;text&gt;c) Charge can be measured and described quantitatively in SI units.&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_pcq_w1d2c_2_1&#34; id=&#34;input_pcq_w1d2c_2_1_choice_4&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_4&#34;/&gt;&lt;label id=&#34;pcq_w1d2c_2_1-choice_4-label&#34; for=&#34;input_pcq_w1d2c_2_1_choice_4&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pcq_w1d2c_2_1&#34;&gt; &lt;text&gt;d) All charges that we can observe directly are integer multiples of some smallest possible amount of charge.&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_pcq_w1d2c_2_1&#34; id=&#34;input_pcq_w1d2c_2_1_choice_5&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_5&#34;/&gt;&lt;label id=&#34;pcq_w1d2c_2_1-choice_5-label&#34; for=&#34;input_pcq_w1d2c_2_1_choice_5&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_pcq_w1d2c_2_1&#34;&gt; &lt;text&gt;e) The coulomb is the basic unit of electricity.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_pcq_w1d2c_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_pcq_w1d2c_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;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_pcq_w1d2c_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Charge is Quantized&#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_pcq_w1d2c&#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_pcq_w1d2c&#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-runtime-version="1" data-block-type="vertical" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="VerticalStudentView" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="False" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-L01v02"> <h2 class="hd hd-2 unit-title">L1v2: Electric Force</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v02"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-runtime-version="1" data-block-type="video" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="False" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v02"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Video"} </script> <h3 class="hd hd-2">L01v02: Electric Force</h3> <div id="video_L01v02" class="video closed" data-metadata='{&#34;showCaptions&#34;: &#34;true&#34;, &#34;speed&#34;: null, &#34;ytMetadataEndpoint&#34;: &#34;&#34;, &#34;recordedYoutubeIsAvailable&#34;: true, &#34;ytTestTimeout&#34;: 1500, &#34;duration&#34;: 0.0, &#34;generalSpeed&#34;: 1.0, &#34;lmsRootURL&#34;: &#34;https://openlearninglibrary.mit.edu&#34;, &#34;autoplay&#34;: false, &#34;transcriptTranslationUrl&#34;: &#34;/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v02/handler/transcript/translation/__lang__&#34;, &#34;transcriptAvailableTranslationsUrl&#34;: &#34;/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v02/handler/transcript/available_translations&#34;, &#34;transcriptLanguages&#34;: {&#34;en&#34;: &#34;English&#34;}, &#34;savedVideoPosition&#34;: 0.0, &#34;completionPercentage&#34;: 0.95, &#34;prioritizeHls&#34;: false, &#34;autohideHtml5&#34;: false, &#34;start&#34;: 0.0, &#34;poster&#34;: null, &#34;streams&#34;: &#34;1.00:GDYfrtBVNLc&#34;, &#34;sources&#34;: [], &#34;saveStateEnabled&#34;: false, &#34;completionEnabled&#34;: false, &#34;saveStateUrl&#34;: &#34;/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v02/handler/xmodule_handler/save_user_state&#34;, &#34;autoAdvance&#34;: false, &#34;transcriptLanguage&#34;: &#34;en&#34;, &#34;publishCompletionUrl&#34;: &#34;/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v02/handler/publish_completion&#34;, &#34;captionDataDir&#34;: null, &#34;end&#34;: 0.0, &#34;ytApiUrl&#34;: &#34;https://www.youtube.com/iframe_api&#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="L01v02"></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_L01v02">Downloads and transcripts</h3> <div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L01v02"> <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+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v02/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+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v02/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-runtime-version="1" data-block-type="vertical" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="VerticalStudentView" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="False" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-CQ-checkpoint_w1_12"> <h2 class="hd hd-2 unit-title">L1Q2: Units of the Coulomb Constant.</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_12"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-runtime-version="1" data-block-type="problem" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="True" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_12"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_checkpoint_w1_12" class="problems-wrapper" role="group" aria-labelledby="checkpoint_w1_12-problem-title" data-problem-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_12" data-url="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_12/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_w1_12-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_12-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Units of the Coulomb Constant &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_12-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/c2f811c5535eb4bf919bbfa48568087f/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_12.svg&#34; width=&#34;330&#34;/&gt; &lt;/center&gt; &lt;p&gt; Consider two point objects of charges [mathjaxinline]q_1&amp;lt;0[/mathjaxinline] and [mathjaxinline]q_2&amp;gt;0[/mathjaxinline] separated a distance [mathjaxinline]r[/mathjaxinline]. The electrostatic force exerted by object 2 on object 1 is given by Coulomb&#39;s law: &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 \displaystyle \vec{F}_{2,1} = k\frac{q_1q_2}{r^2}\hat{r}_{2,1}[/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; where [mathjaxinline]\hat{r}_{2,1}[/mathjaxinline] is the unit vector directed along the line joining the two objects pointing from charge 2 to charge 1, and [mathjaxinline]k[/mathjaxinline] is the Coulomb constant. The value of the Coulomb constant in SI units is approximately [mathjaxinline]9\times 10^9[/mathjaxinline] and the units are: &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_w1_12_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_checkpoint_w1_12_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_checkpoint_w1_12_2_1&#34; id=&#34;input_checkpoint_w1_12_2_1_choice_1&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;checkpoint_w1_12_2_1-choice_1-label&#34; for=&#34;input_checkpoint_w1_12_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w1_12_2_1&#34;&gt; &lt;text&gt; [mathjaxinline]k \approx 9\times 10^9 \frac{\mbox{N}\cdot \mbox{C}^2}{\mbox{m}^2}[/mathjaxinline]&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_w1_12_2_1&#34; id=&#34;input_checkpoint_w1_12_2_1_choice_2&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;checkpoint_w1_12_2_1-choice_2-label&#34; for=&#34;input_checkpoint_w1_12_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w1_12_2_1&#34;&gt; &lt;text&gt; [mathjaxinline]k \approx 9\times 10^9 \frac{\mbox{N}\cdot \mbox{m}^2}{\mbox{C}^2}[/mathjaxinline]&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_w1_12_2_1&#34; id=&#34;input_checkpoint_w1_12_2_1_choice_3&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;checkpoint_w1_12_2_1-choice_3-label&#34; for=&#34;input_checkpoint_w1_12_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w1_12_2_1&#34;&gt; &lt;text&gt; [mathjaxinline]k \approx 9\times 10^9 \frac{\mbox{C}^2\cdot \mbox{m}^2}{\mbox{N}}[/mathjaxinline]&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_w1_12_2_1&#34; id=&#34;input_checkpoint_w1_12_2_1_choice_4&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_4&#34;/&gt;&lt;label id=&#34;checkpoint_w1_12_2_1-choice_4-label&#34; for=&#34;input_checkpoint_w1_12_2_1_choice_4&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w1_12_2_1&#34;&gt; &lt;text&gt; [mathjaxinline]k \approx 9\times 10^9 \frac{\mbox{N}\cdot \mbox{m}}{\mbox{C}^2}[/mathjaxinline]&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_checkpoint_w1_12_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_w1_12_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_w1_12_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;Units of the Coulomb Constant&#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_w1_12&#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_w1_12&#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-runtime-version="1" data-block-type="vertical" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="VerticalStudentView" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="False" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-L01v03"> <h2 class="hd hd-2 unit-title">L1v3: Rewrite the Unit Vector in Coulomb&#39;s Law</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@html+block@lesson01_01"> <div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-runtime-version="1" data-block-type="html" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="False" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@html+block@lesson01_01"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "HTMLModule"} </script> <p><b>Unit vectors and Coulomb's law. </b></p><p><center><img src="/assets/courseware/v1/907131dd83f657d4bef68fb58a4cb129/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_html_lesson1_unit_vectors_a.svg" width="300"/></center></p><p>Consider two objects of charges \(q_1\) and \(q_2\) shown in the figure above, \(\hat{r}_{1,2}\) is the unit vector directed along the line joining the two object that points from object 1 to object 2.</p><p><center><img src="/assets/courseware/v1/65f61430e8359160e1762742c2d9bbce/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_html_lesson1_unit_vectors_b.svg" width="300"/></center></p><p> If \(\vec{r}_{1,2}\) is the position of object 2 measured from 1, shown above, the unit vector, \(\hat{r}_{1,2}\) can be expressed as:</p><p> \[\displaystyle \hat{r}_{1,2} = \frac{\vec{r}_{1,2}}{|\vec{r}_{1,2}|}\]</p><p>The electrostatic force exerted by object 1 on 2 is expressed in terms of the unit vector \(\hat{r}_{1,2}\) as:</p><p> \[\displaystyle \vec{F}_{1,2} = kq_1q_2\frac{\hat{r}_{1,2}}{|\vec{r}_{1,2}|^2}\] </p><p>and in terms of the vector \(\vec{r}_{1,2}\) the Coulomb force is given by:</p><p> \[\displaystyle \vec{F}_{1,2} = kq_1q_2\frac{\vec{r}_{1,2}}{|\vec{r}_{1,2}|^3}\] </p><p><b>Note:</b> In the second expression, the force is divided by the distance cubed but the magnitude of the force still follows an inverse square distance law.</p> </div> </div> <div class="vert vert-1" data-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v03"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-runtime-version="1" data-block-type="video" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="XBlockToXModuleShim" 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<div class="xblock xblock-public_view xblock-public_view-vertical" data-runtime-version="1" data-block-type="vertical" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="VerticalStudentView" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="False" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-l01Q03"> <h2 class="hd hd-2 unit-title">L1Q3: Unit Vector Calculation and Force Between two Charges.</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_13"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-runtime-version="1" data-block-type="problem" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="True" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_13"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_checkpoint_w1_13" class="problems-wrapper" role="group" aria-labelledby="checkpoint_w1_13-problem-title" data-problem-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_13" data-url="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_13/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="3.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;checkpoint_w1_13-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_13-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Unit vector calculation. &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_13-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/ce5c75153d525a9fbd8de252238ad191/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_7.svg&#34; width=&#34;330&#34;/&gt; &lt;/center&gt; &lt;p&gt; Two charged objects are separated a distance [mathjaxinline]d[/mathjaxinline] as shown. The angle between the line joining the objects and the horizontal is [mathjaxinline]30^\circ[/mathjaxinline]. Consider the (x,y) coordinate system with origin at the location of object 2. &lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part a)&lt;/b&gt; Calculate [mathjaxinline]\vec{r}_{2,1}[/mathjaxinline], the position vector of object 1 measured from object 2. Express your answer in terms of hati for [mathjaxinline]\hat{i}[/mathjaxinline], hatj for [mathjaxinline]\hat{j}[/mathjaxinline], and [mathjaxinline]d[/mathjaxinline] as needed. Remember that the argument of [mathjaxinline]\sin[/mathjaxinline] and [mathjaxinline]\cos[/mathjaxinline] in answer boxes needs to be entered in radians. &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]\vec{r}_{2,1}=[/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_checkpoint_w1_13_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_checkpoint_w1_13_2_1&#34; id=&#34;input_checkpoint_w1_13_2_1&#34; aria-describedby=&#34;status_checkpoint_w1_13_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;35&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_checkpoint_w1_13_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_checkpoint_w1_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;p id=&#34;answer_checkpoint_w1_13_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_checkpoint_w1_13_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_checkpoint_w1_13_2_1_dynamath&#34; name=&#34;input_checkpoint_w1_13_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_checkpoint_w1_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; Calculate [mathjaxinline]\hat{r}_{2,1}[/mathjaxinline], the unit vector pointing in the direction from object 2 to object 1. Express your answer in terms of hati for [mathjaxinline]\hat{i}[/mathjaxinline], hatj for [mathjaxinline]\hat{j}[/mathjaxinline], and [mathjaxinline]d[/mathjaxinline] as needed. &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]\hat{r}_{2,1}=[/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_checkpoint_w1_13_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_checkpoint_w1_13_3_1&#34; id=&#34;input_checkpoint_w1_13_3_1&#34; aria-describedby=&#34;status_checkpoint_w1_13_3_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;35&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_checkpoint_w1_13_3_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_checkpoint_w1_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;p id=&#34;answer_checkpoint_w1_13_3_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_checkpoint_w1_13_3_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_checkpoint_w1_13_3_1_dynamath&#34; name=&#34;input_checkpoint_w1_13_3_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_checkpoint_w1_13_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; Calculate the force on object 1 due to the interaction with object 2. Express your answer in terms of hati for [mathjaxinline]\hat{i}[/mathjaxinline], hatj for [mathjaxinline]\hat{j}[/mathjaxinline], [mathjaxinline]d[/mathjaxinline], [mathjaxinline]k[/mathjaxinline], q_1 for [mathjaxinline]q_1[/mathjaxinline] and q_2 for [mathjaxinline]q_2[/mathjaxinline] as needed. &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]\vec{F}_{2,1}=[/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_checkpoint_w1_13_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_checkpoint_w1_13_4_1&#34; id=&#34;input_checkpoint_w1_13_4_1&#34; aria-describedby=&#34;status_checkpoint_w1_13_4_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;35&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_checkpoint_w1_13_4_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_checkpoint_w1_13_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_checkpoint_w1_13_4_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_checkpoint_w1_13_4_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_checkpoint_w1_13_4_1_dynamath&#34; name=&#34;input_checkpoint_w1_13_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_checkpoint_w1_13_solution_3&#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;Unit vector calculation.&#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_w1_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_w1_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-runtime-version="1" data-block-type="vertical" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="VerticalStudentView" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="False" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-W01D2-04"> <h2 class="hd hd-2 unit-title">Superposition of Coulomb&#39;s Law.</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@html+block@lesson01_02"> <div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-runtime-version="1" data-block-type="html" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="False" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@html+block@lesson01_02"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "HTMLModule"} </script> <p><b>Superposition Principle. </b></p><p>Coulomb's law applies to any pair of point charges. When more than two charges are present, the total force on any one charge is the vector sum of the forces exerted on it by the other charges. For example, if three charges \(q_1\), \(q_2\) and \(q_3\) are present, the resultant force experienced by charge charge 3 is: .</p><p> \[ \vec{F}_{3} = \vec{F}_{1,3} + \vec{F}_{2,3} \] </p><p><center><img src="/assets/courseware/v1/b5babbeff5fd0e29b04b07e7e12ea27d/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_html_lesson1_superposition.svg" width="300"/></center></p> </div> </div> </div> </div>

<div class="xblock xblock-public_view xblock-public_view-vertical" data-runtime-version="1" data-block-type="vertical" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="VerticalStudentView" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="False" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-L01v04"> <h2 class="hd hd-2 unit-title">L1v4: Worked Example - Total Force on a Charged Object</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_15"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-runtime-version="1" data-block-type="problem" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="True" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_15"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_checkpoint_w1_15" class="problems-wrapper" role="group" aria-labelledby="checkpoint_w1_15-problem-title" data-problem-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_15" data-url="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_15/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;checkpoint_w1_15-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_15-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Worked Example: Total force on a charged object. &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_15-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/v1/0e49e5bf2b456cd63bb02b7310eb3d43/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_15.svg&#34; width=&#34;440&#34;/&gt; &lt;/center&gt; &lt;p&gt; Three charged objects of charges [mathjaxinline]q_1[/mathjaxinline], [mathjaxinline]q_2[/mathjaxinline] and [mathjaxinline]q_3[/mathjaxinline] are located at the vertices of an isosceles triangles of base [mathjaxinline]2s[/mathjaxinline] and height [mathjaxinline]d[/mathjaxinline]. Assume [mathjaxinline]q_1=q_3=+Q[/mathjaxinline] and [mathjaxinline]q_2=-Q[/mathjaxinline], where [mathjaxinline]Q &amp;gt;0[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; Calculate, [mathjaxinline]\vec{F}_{2}[/mathjaxinline], the force exerted by objects 1 and 3 on object 2. Express your answer in terms of [mathjaxinline]k[/mathjaxinline], [mathjaxinline]Q[/mathjaxinline], [mathjaxinline]s[/mathjaxinline], [mathjaxinline]d[/mathjaxinline], hati for [mathjaxinline]\hat{i}[/mathjaxinline] and hatj for [mathjaxinline]\hat{j}[/mathjaxinline] as needed. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]\vec{F}_{2}=[/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_checkpoint_w1_15_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_checkpoint_w1_15_2_1&#34; id=&#34;input_checkpoint_w1_15_2_1&#34; aria-describedby=&#34;status_checkpoint_w1_15_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;35&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_checkpoint_w1_15_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_checkpoint_w1_15_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_checkpoint_w1_15_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_checkpoint_w1_15_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_checkpoint_w1_15_2_1_dynamath&#34; name=&#34;input_checkpoint_w1_15_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_checkpoint_w1_15_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;Worked Example: Total force on a charged object.&#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_w1_15&#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_w1_15&#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_w1_15-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_w1_15-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_w1_15-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 class="vert vert-1" data-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v04"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-runtime-version="1" data-block-type="video" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="False" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v04"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Video"} </script> <h3 class="hd hd-2">L01v04: Worked Example - Total Force on a Charged Object</h3> <div id="video_L01v04" class="video closed" data-metadata='{&#34;showCaptions&#34;: &#34;true&#34;, &#34;speed&#34;: null, &#34;ytMetadataEndpoint&#34;: &#34;&#34;, &#34;recordedYoutubeIsAvailable&#34;: true, &#34;ytTestTimeout&#34;: 1500, &#34;duration&#34;: 383.02, &#34;generalSpeed&#34;: 1.0, &#34;lmsRootURL&#34;: &#34;https://openlearninglibrary.mit.edu&#34;, &#34;autoplay&#34;: false, &#34;transcriptTranslationUrl&#34;: &#34;/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v04/handler/transcript/translation/__lang__&#34;, &#34;transcriptAvailableTranslationsUrl&#34;: &#34;/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v04/handler/transcript/available_translations&#34;, &#34;transcriptLanguages&#34;: {&#34;en&#34;: &#34;English&#34;}, &#34;savedVideoPosition&#34;: 0.0, &#34;completionPercentage&#34;: 0.95, &#34;prioritizeHls&#34;: false, &#34;autohideHtml5&#34;: false, &#34;start&#34;: 0.0, &#34;poster&#34;: &#34;https://mitx-edx-video-meta-storage.s3.amazonaws.com/media/video-images/22da5c1cca1848adbb94d298950df8d0.png?AWSAccessKeyId=ASIA4QDFFSUR5HNT23XG&amp;Expires=1732403197&amp;Signature=jZ4kAEBzuJ1qrCi5E8ihUpJlErY%3D&amp;x-amz-security-token=IQoJb3JpZ2luX2VjEEcaCXVzLWVhc3QtMSJGMEQCIHMihQlMd%2Bijb2oNQwYWtISz0FVfrTnfIhRrIDTBC2C0AiA8ENO4D9CnrnF0sKayZS%2FHGGIxBDOWs2QgdZC%2BURZKdyrFBQjg%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAMaDDg1OTIwNTYzNzQxMSIM05LDLlOuzlrggAalKpkFK0p0U05O%2Fvfg0lPrcd1f2HT9IFZFiSnObdhVjwvb6VjnZ03d6Agw3nvpF7AX51Y61AWx12ziB20wtMqJNjzcJvNG50uxYo5YQz8ypQF9Ypm0gFWaIFBiD1%2Bnxf8o244ON2ziuYynW3SPs02tBU3A3at8behZOBVCiagHnBXf4D4OHg%2BropPhYc0ewl01xiNJwXDEVN3tGTvJGVbogHXHJA9WbSe9hNPXev5Qb1m6TLXOiR00cSKymvNwq%2B87G2KPv6KewLfz6jV7Xao9BOgq59it3ifVwNIgbRVKwe%2FXswfLJQDvHGNZutdgKxmnElD47QNpxs62Jry7w53Me4ckCS1q4uzWxvhHww6dvoSpvAXJqVMzb%2BfLJ8Z1lUSK8An4utUTgVJJ5ShRRQ%2FYqbJs67fLCQFlO9RU498mgiJAKWX2uULSLEhhpYD3YL1Ehi09w4JIt1EqSTp62LSsIbF2FdLK5ZyrH0pkgDHJ43gRHyXc22DYPZTJWdvIGTket64oR%2BnPJ9i6ZkL1VwWU5vRFnwZcw%2B8b2%2B9QcAyQaac78FpI2zmU0ZT3epBPGhZpe1sRgWvSnY6LsTY%2BuK5pza4Y%2BfdXpQPEC7%2FRTeTFnWRS4Fjh1AAEC2SHqV%2BDPuYD2SuzD31tqdG9ZGgia6bIpETBBt1lxxNCriDawq%2BpFxMUIMSjkckaGI%2F4AhV59%2Bba0INa62KrDsUwGmO4VVD5EpHuTDxyI2cpCmrrvxG27Bsdro8jnXFzAumU5MKUD%2B64NDdBRCZ7F4VzuFeG2rdyo2xi0fOwd0htFs7OmMcydEq%2Ft0erwGANuhe08mtbybD3ldF4lUOsBm8k7x5SnvKgFvaTaQSd7N4q7%2FuFZXsJWpCJH36vxJsxiWGBuIgw2ruJugY6sgEB7NTMh%2FM2IDdtofd818pgY9ZonhE9f468Hf2sF6SMylE9tWltUPZiY1ZlHIIBalJAglU3WErhqlvLxVgiH3vJDC3GyOhoaAV2pJczx8ozPWpg3V8zFXBvX3t%2BGCuLoCvE8VAwS9d2XLLJ60DvYppS5qbgtiBdPaZJnel2O%2BXQNKSMBouIRft8UA5exSBARjn3%2FR1wNIUglP1QQzM6eagXfQtCi3tx8JnXoBLZQdFctH%2FT&#34;, &#34;streams&#34;: &#34;1.00:N4oQjZMaICM&#34;, &#34;sources&#34;: [&#34;https://d2f1egay8yehza.cloudfront.net/MIT8021E2018-V000900_DTH.mp4&#34;, &#34;https://d2f1egay8yehza.cloudfront.net/MIT8021E2018-V000900/MIT8021E2018-V000900.m3u8&#34;], &#34;saveStateEnabled&#34;: false, &#34;completionEnabled&#34;: false, &#34;saveStateUrl&#34;: &#34;/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v04/handler/xmodule_handler/save_user_state&#34;, &#34;autoAdvance&#34;: false, &#34;transcriptLanguage&#34;: &#34;en&#34;, &#34;publishCompletionUrl&#34;: &#34;/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v04/handler/publish_completion&#34;, &#34;captionDataDir&#34;: null, &#34;end&#34;: 0.0, &#34;ytApiUrl&#34;: &#34;https://www.youtube.com/iframe_api&#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="L01v04"></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. 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<div class="xblock xblock-public_view xblock-public_view-vertical" data-runtime-version="1" data-block-type="vertical" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="VerticalStudentView" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="False" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-exam1rev-cq2"> <h2 class="hd hd-2 unit-title">L1Q4: Direction of the Total Force.</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@exam1rev-cq2"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-runtime-version="1" data-block-type="problem" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="True" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@exam1rev-cq2"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_exam1rev-cq2" class="problems-wrapper" role="group" aria-labelledby="exam1rev-cq2-problem-title" data-problem-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@exam1rev-cq2" data-url="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@problem+block@exam1rev-cq2/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;exam1rev-cq2-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.1x+1T2019+type@problem+block@exam1rev-cq2-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Direction of the Total Force &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.1x+1T2019+type@problem+block@exam1rev-cq2-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/d8638e7fd0113b51208eab65cfb9309e/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_exam1rev-cq2_fig1.svg&#34; width=&#34;330&#34;/&gt; &lt;/center&gt; &lt;p&gt; Three point-like charged objects are fixed on three corners of a square of side [mathjaxinline]a[/mathjaxinline]. The object at point [mathjaxinline]A[/mathjaxinline] has charge [mathjaxinline]-Q[/mathjaxinline], the object at point [mathjaxinline]B[/mathjaxinline] has charge [mathjaxinline]+Q[/mathjaxinline], and the object at point [mathjaxinline]C[/mathjaxinline] has charge [mathjaxinline]+Q[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; Which of the arrows below best represents the approximate direction of the total force on the charge at point [mathjaxinline]C[/mathjaxinline]? &lt;/p&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/61aca18d33c1dd8f9be43138b21ac15f/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_exam1rev-cq2_fig2.svg&#34; width=&#34;550&#34;/&gt; &lt;/center&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_exam1rev-cq2_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_exam1rev-cq2_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_exam1rev-cq2_2_1&#34; id=&#34;input_exam1rev-cq2_2_1_choice_1&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;exam1rev-cq2_2_1-choice_1-label&#34; for=&#34;input_exam1rev-cq2_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_exam1rev-cq2_2_1&#34;&gt; &lt;text&gt; (1)&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_exam1rev-cq2_2_1&#34; id=&#34;input_exam1rev-cq2_2_1_choice_2&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;exam1rev-cq2_2_1-choice_2-label&#34; for=&#34;input_exam1rev-cq2_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_exam1rev-cq2_2_1&#34;&gt; &lt;text&gt; (2)&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_exam1rev-cq2_2_1&#34; id=&#34;input_exam1rev-cq2_2_1_choice_3&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;exam1rev-cq2_2_1-choice_3-label&#34; for=&#34;input_exam1rev-cq2_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_exam1rev-cq2_2_1&#34;&gt; &lt;text&gt; (3)&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_exam1rev-cq2_2_1&#34; id=&#34;input_exam1rev-cq2_2_1_choice_4&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_4&#34;/&gt;&lt;label id=&#34;exam1rev-cq2_2_1-choice_4-label&#34; for=&#34;input_exam1rev-cq2_2_1_choice_4&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_exam1rev-cq2_2_1&#34;&gt; &lt;text&gt; (4)&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_exam1rev-cq2_2_1&#34; id=&#34;input_exam1rev-cq2_2_1_choice_5&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_5&#34;/&gt;&lt;label id=&#34;exam1rev-cq2_2_1-choice_5-label&#34; for=&#34;input_exam1rev-cq2_2_1_choice_5&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_exam1rev-cq2_2_1&#34;&gt; &lt;text&gt; (5)&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_exam1rev-cq2_2_1&#34; id=&#34;input_exam1rev-cq2_2_1_choice_6&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_6&#34;/&gt;&lt;label id=&#34;exam1rev-cq2_2_1-choice_6-label&#34; for=&#34;input_exam1rev-cq2_2_1_choice_6&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_exam1rev-cq2_2_1&#34;&gt; &lt;text&gt; (6)&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_exam1rev-cq2_2_1&#34; id=&#34;input_exam1rev-cq2_2_1_choice_7&#34; 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<div class="xblock xblock-public_view xblock-public_view-vertical" data-runtime-version="1" data-block-type="vertical" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="VerticalStudentView" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="False" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-checkpoint-l01Q05"> <h2 class="hd hd-2 unit-title">L1Q5: Charges on a Triangle.</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_6"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-runtime-version="1" data-block-type="problem" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="True" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_6"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_checkpoint_w1_6" class="problems-wrapper" role="group" aria-labelledby="checkpoint_w1_6-problem-title" data-problem-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_6" data-url="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_6/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_w1_6-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_6-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Charges on a triangle. &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_6-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/v1/6bcb7eec5496cd1c7a87a44af9949dca/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_6.svg&#34; width=&#34;550&#34;/&gt; &lt;/center&gt; &lt;p&gt; Three point like objects of charges [mathjaxinline]q_1=-2q[/mathjaxinline], [mathjaxinline]q_2=+q[/mathjaxinline], and [mathjaxinline]q_3=-q[/mathjaxinline] (where [mathjaxinline]q[/mathjaxinline] is positive) are glued to the vertices of an equilateral triangle of side [mathjaxinline]a[/mathjaxinline] as shown. Consider the coordinate system indicated in the figure. &lt;/p&gt; &lt;p&gt; Calculate, [mathjaxinline]\vec{F}_{3}[/mathjaxinline], the force exerted by objects 1 and 2 on object 3. Express your answer in terms of [mathjaxinline]k[/mathjaxinline], [mathjaxinline]q[/mathjaxinline], [mathjaxinline]a[/mathjaxinline], hati for [mathjaxinline]\hat{i}[/mathjaxinline] and hatj for [mathjaxinline]\hat{j}[/mathjaxinline] as needed. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]\vec{F}_{3}=[/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_checkpoint_w1_6_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_checkpoint_w1_6_2_1&#34; id=&#34;input_checkpoint_w1_6_2_1&#34; aria-describedby=&#34;status_checkpoint_w1_6_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;35&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_checkpoint_w1_6_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_checkpoint_w1_6_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_checkpoint_w1_6_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_checkpoint_w1_6_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_checkpoint_w1_6_2_1_dynamath&#34; name=&#34;input_checkpoint_w1_6_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_checkpoint_w1_6_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;Charges on a triangle.&#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_w1_6&#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_w1_6&#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;span class=&#34;problem-action-button-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;save problem-action-btn btn-default btn-small&#34; data-value=&#34;Save&#34;&gt; &lt;span class=&#34;icon fa fa-floppy-o&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span aria-hidden=&#34;true&#34;&gt;Save&lt;/span&gt; &lt;span class=&#34;sr&#34;&gt;Save your answer&lt;/span&gt; &lt;/button&gt; &lt;/span&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_w1_6-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_w1_6-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_w1_6-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-runtime-version="1" data-block-type="vertical" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="VerticalStudentView" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="False" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-L01v05"> <h2 class="hd hd-2 unit-title">L1v5: Analogy of Coulomb&#39;s Law and Gravity</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v05"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-runtime-version="1" data-block-type="video" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="False" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v05"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Video"} </script> <h3 class="hd hd-2">L01v05: Analogy of Coulomb&#39;s Law and Gravity</h3> <div id="video_L01v05" class="video closed" data-metadata='{&#34;showCaptions&#34;: &#34;true&#34;, &#34;speed&#34;: null, &#34;ytMetadataEndpoint&#34;: &#34;&#34;, &#34;recordedYoutubeIsAvailable&#34;: true, &#34;ytTestTimeout&#34;: 1500, &#34;duration&#34;: 0.0, &#34;generalSpeed&#34;: 1.0, &#34;lmsRootURL&#34;: &#34;https://openlearninglibrary.mit.edu&#34;, &#34;autoplay&#34;: false, &#34;transcriptTranslationUrl&#34;: &#34;/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v05/handler/transcript/translation/__lang__&#34;, &#34;transcriptAvailableTranslationsUrl&#34;: &#34;/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v05/handler/transcript/available_translations&#34;, &#34;transcriptLanguages&#34;: {&#34;en&#34;: &#34;English&#34;}, &#34;savedVideoPosition&#34;: 0.0, &#34;completionPercentage&#34;: 0.95, &#34;prioritizeHls&#34;: false, &#34;autohideHtml5&#34;: false, &#34;start&#34;: 0.0, &#34;poster&#34;: null, &#34;streams&#34;: &#34;1.00:97V_RVuVvG4&#34;, &#34;sources&#34;: [], &#34;saveStateEnabled&#34;: false, &#34;completionEnabled&#34;: false, &#34;saveStateUrl&#34;: &#34;/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v05/handler/xmodule_handler/save_user_state&#34;, &#34;autoAdvance&#34;: false, &#34;transcriptLanguage&#34;: &#34;en&#34;, &#34;publishCompletionUrl&#34;: &#34;/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v05/handler/publish_completion&#34;, &#34;captionDataDir&#34;: null, &#34;end&#34;: 0.0, &#34;ytApiUrl&#34;: &#34;https://www.youtube.com/iframe_api&#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="L01v05"></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_L01v05">Downloads and transcripts</h3> <div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L01v05"> <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+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v05/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+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L01v05/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-runtime-version="1" data-block-type="vertical" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="VerticalStudentView" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="False" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-checkpoint-L1Q06"> <h2 class="hd hd-2 unit-title">L1Q6: Gravitational Force vs. Electric Force. </h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_8"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-runtime-version="1" data-block-type="problem" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="True" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_8"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_checkpoint_w1_8" class="problems-wrapper" role="group" aria-labelledby="checkpoint_w1_8-problem-title" data-problem-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_8" data-url="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_8/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_w1_8-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_8-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Gravitational force vs. electric force. &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_8-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; The goal of this question is to compare [mathjaxinline]|\vec{F}_ G|[/mathjaxinline], the magnitude of the gravitational attraction between two protons with [mathjaxinline]|\vec{F}_ E|[/mathjaxinline], the magnitude of the electrostatic repulsion between them. &lt;/p&gt; &lt;p&gt; You might find the following constants useful: the mass of a proton [mathjaxinline]m_ p= 1.67\times 10^{-27}\; \mbox{kg}[/mathjaxinline], the gravitational constant [mathjaxinline]G= 6.67\times 10^{-11\, } \mbox{N}\; \mbox{m}^2\; \mbox{kg}^{-2}[/mathjaxinline], the charge of the proton [mathjaxinline]e= 1.6 \times 10^{-19} \mbox{C}[/mathjaxinline], and the Coulomb constant [mathjaxinline]k=9\times 10^9 \; \mbox{N}\; \mbox{m}^2\; \mbox{C}^{-2}[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; Consider two protons a distance [mathjaxinline]d=10^{-15} \mbox{m}[/mathjaxinline] apart, the order of magnitude of the ratio [mathjaxinline]|\vec{F}_ G|/|\vec{F}_ E|[/mathjaxinline] 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_checkpoint_w1_8_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_checkpoint_w1_8_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_checkpoint_w1_8_2_1&#34; id=&#34;input_checkpoint_w1_8_2_1_choice_1&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;checkpoint_w1_8_2_1-choice_1-label&#34; for=&#34;input_checkpoint_w1_8_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w1_8_2_1&#34;&gt; &lt;text&gt; [mathjaxinline]|\vec{F}_ G|/|\vec{F}_ E|\approx 10^{6}[/mathjaxinline]&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_w1_8_2_1&#34; id=&#34;input_checkpoint_w1_8_2_1_choice_2&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;checkpoint_w1_8_2_1-choice_2-label&#34; for=&#34;input_checkpoint_w1_8_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w1_8_2_1&#34;&gt; &lt;text&gt; [mathjaxinline]|\vec{F}_ G|/|\vec{F}_ E|\approx 10^{36}[/mathjaxinline]&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_w1_8_2_1&#34; id=&#34;input_checkpoint_w1_8_2_1_choice_3&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;checkpoint_w1_8_2_1-choice_3-label&#34; for=&#34;input_checkpoint_w1_8_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w1_8_2_1&#34;&gt; &lt;text&gt; [mathjaxinline]|\vec{F}_ G|/|\vec{F}_ E|\approx 10^{-36}[/mathjaxinline]&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_w1_8_2_1&#34; id=&#34;input_checkpoint_w1_8_2_1_choice_4&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_4&#34;/&gt;&lt;label id=&#34;checkpoint_w1_8_2_1-choice_4-label&#34; for=&#34;input_checkpoint_w1_8_2_1_choice_4&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w1_8_2_1&#34;&gt; &lt;text&gt; [mathjaxinline]|\vec{F}_ G|/|\vec{F}_ E|\approx 10^{-6}[/mathjaxinline]&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_w1_8_2_1&#34; id=&#34;input_checkpoint_w1_8_2_1_choice_5&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_5&#34;/&gt;&lt;label id=&#34;checkpoint_w1_8_2_1-choice_5-label&#34; for=&#34;input_checkpoint_w1_8_2_1_choice_5&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w1_8_2_1&#34;&gt; &lt;text&gt; None of the above.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_checkpoint_w1_8_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_w1_8_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_w1_8_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;Gravitational force vs. electric force.&#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_w1_8&#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_w1_8&#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;span class=&#34;problem-action-button-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;save problem-action-btn btn-default btn-small&#34; data-value=&#34;Save&#34;&gt; &lt;span class=&#34;icon fa fa-floppy-o&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span aria-hidden=&#34;true&#34;&gt;Save&lt;/span&gt; &lt;span class=&#34;sr&#34;&gt;Save your answer&lt;/span&gt; &lt;/button&gt; &lt;/span&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_w1_8-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_w1_8-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_w1_8-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 class="vert vert-1" data-id="block-v1:MITx+8.02.1x+1T2019+type@html+block@pset_pset1_1"> <div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-runtime-version="1" data-block-type="html" data-runtime-class="LmsRuntime" data-request-token="e41eeb28a9ee11efb24a16fffa68ec97" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-has-score="False" data-graded="True" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@html+block@pset_pset1_1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "HTMLModule"} </script> <p>Helpful content from the textbook can be found in Chapter 2, <a href="/courses/course-v1:MITx+8.02.1x+1T2019/pdfbook/0/chapter/2/3" target="_blank">Section 2.2</a> and <a href="/courses/course-v1:MITx+8.02.1x+1T2019/pdfbook/0/chapter/2/37" target="_blank">Example 2.14.1</a>.</p> </div> </div> </div> </div>