<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="14942a64ea7411efb8100e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-lesson06b-textbooklinks" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="vertical" data-init="VerticalStudentView" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-runtime-class="LmsRuntime">
<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-lesson06b-textbooklinks">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-request-token="14942a64ea7411efb8100e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@html+block@html-lesson06b-textbooklinks" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="html" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<p> We continue to use Gauss's Law to calculate the Electric Field for cases with specific symmetries - namely cylindrical and spherical.</p><p> Textbook Links </p><ul><li><a href="/courses/course-v1:MITx+8.02.1x+1T2019/pdfbook/0/chapter/3/11">Chapter 3.2 Gauss's Law</a></li></ul>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="14942a64ea7411efb8100e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-L06bv01" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="vertical" data-init="VerticalStudentView" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-runtime-class="LmsRuntime">
<h2 class="hd hd-2 unit-title">L6bv1: Electric Field of an Infinite Wire</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv01">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-request-token="14942a64ea7411efb8100e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv01" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="video" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">L06bv01: Electric Field of an Infinite Wire</h3>
<div
id="video_L06bv01"
class="video closed"
data-metadata='{"saveStateUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv01/handler/xmodule_handler/save_user_state", "completionEnabled": false, "ytTestTimeout": 1500, "autohideHtml5": false, "completionPercentage": 0.95, "poster": null, "ytApiUrl": "https://www.youtube.com/iframe_api", "sources": [], "transcriptLanguages": {"en": "English"}, "saveStateEnabled": false, "captionDataDir": null, "recordedYoutubeIsAvailable": true, "autoAdvance": false, "duration": 0.0, "publishCompletionUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv01/handler/publish_completion", "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv01/handler/transcript/translation/__lang__", "prioritizeHls": false, "autoplay": false, "savedVideoPosition": 0.0, "streams": "1.00:YaXRT0SbpUM", "speed": null, "generalSpeed": 1.0, "ytMetadataEndpoint": "", "showCaptions": "true", "start": 0.0, "transcriptLanguage": "en", "lmsRootURL": "https://openlearninglibrary.mit.edu", "end": 0.0, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv01/handler/transcript/available_translations"}'
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="L06bv01"></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_L06bv01">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L06bv01">
<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@L06bv01/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@L06bv01/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-request-token="14942a64ea7411efb8100e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-L06bv02" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="vertical" data-init="VerticalStudentView" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-runtime-class="LmsRuntime">
<h2 class="hd hd-2 unit-title">L6bv2: Electric Field of an Infinite Cylinder</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv02">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-request-token="14942a64ea7411efb8100e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv02" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="video" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">L06bv02: Electric Field of an Infinite Cylinder</h3>
<div
id="video_L06bv02"
class="video closed"
data-metadata='{"saveStateUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv02/handler/xmodule_handler/save_user_state", "completionEnabled": false, "ytTestTimeout": 1500, "autohideHtml5": false, "completionPercentage": 0.95, "poster": null, "ytApiUrl": "https://www.youtube.com/iframe_api", "sources": [], "transcriptLanguages": {"en": "English"}, "saveStateEnabled": false, "captionDataDir": null, "recordedYoutubeIsAvailable": true, "autoAdvance": false, "duration": 0.0, "publishCompletionUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv02/handler/publish_completion", "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv02/handler/transcript/translation/__lang__", "prioritizeHls": false, "autoplay": false, "savedVideoPosition": 0.0, "streams": "1.00:p9gtBVSJVAQ", "speed": null, "generalSpeed": 1.0, "ytMetadataEndpoint": "", "showCaptions": "true", "start": 0.0, "transcriptLanguage": "en", "lmsRootURL": "https://openlearninglibrary.mit.edu", "end": 0.0, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv02/handler/transcript/available_translations"}'
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="L06bv02"></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_L06bv02">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L06bv02">
<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@L06bv02/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@L06bv02/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-request-token="14942a64ea7411efb8100e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-L06bv03" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="vertical" data-init="VerticalStudentView" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-runtime-class="LmsRuntime">
<h2 class="hd hd-2 unit-title">L6bv3: Electric Field of a Non-uniform Infinite Cylinder</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv03">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-request-token="14942a64ea7411efb8100e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv03" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="video" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">L06bv03: Electric Field of a Non-uniform Infinite Cylinder</h3>
<div
id="video_L06bv03"
class="video closed"
data-metadata='{"saveStateUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv03/handler/xmodule_handler/save_user_state", "completionEnabled": false, "ytTestTimeout": 1500, "autohideHtml5": false, "completionPercentage": 0.95, "poster": null, "ytApiUrl": "https://www.youtube.com/iframe_api", "sources": [], "transcriptLanguages": {"en": "English"}, "saveStateEnabled": false, "captionDataDir": null, "recordedYoutubeIsAvailable": true, "autoAdvance": false, "duration": 0.0, "publishCompletionUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv03/handler/publish_completion", "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv03/handler/transcript/translation/__lang__", "prioritizeHls": false, "autoplay": false, "savedVideoPosition": 0.0, "streams": "1.00:hxuQas6P8mA", "speed": null, "generalSpeed": 1.0, "ytMetadataEndpoint": "", "showCaptions": "true", "start": 0.0, "transcriptLanguage": "en", "lmsRootURL": "https://openlearninglibrary.mit.edu", "end": 0.0, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv03/handler/transcript/available_translations"}'
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="L06bv03"></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_L06bv03">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L06bv03">
<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@L06bv03/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@L06bv03/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-request-token="14942a64ea7411efb8100e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@L6bQ3" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="vertical" data-init="VerticalStudentView" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-runtime-class="LmsRuntime">
<h2 class="hd hd-2 unit-title">L6bQ1: E-field Outside Non-uniform Cylinder</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w3_6">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="14942a64ea7411efb8100e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w3_6" data-graded="True" data-has-score="True" data-runtime-version="1" data-block-type="problem" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_checkpoint_w3_6" class="problems-wrapper" role="group"
aria-labelledby="checkpoint_w3_6-problem-title"
data-problem-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w3_6" data-url="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w3_6/handler/xmodule_handler"
data-problem-score="0.0"
data-problem-total-possible="1.0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="checkpoint_w3_6-problem-title" aria-describedby="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w3_6-problem-progress" tabindex="-1">
Electric field of a non uniform charged cylinder.
</h3>
<div class="problem-progress" id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w3_6-problem-progress"></div>
<div class="problem">
<div>
<center>
<img src="/assets/courseware/v1/929d175df305618a4897e6e9f70ffcc5/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w3_6.svg" width="550"/>
</center>
<p>
An infinitely long and non-conducting cylinder of radius [mathjaxinline]a[/mathjaxinline] has a volume charge density [mathjaxinline]\rho = br[/mathjaxinline] where [mathjaxinline]b[/mathjaxinline] is a positive constant of units (C[mathjaxinline]\cdot[/mathjaxinline]m[mathjaxinline]^{-4}[/mathjaxinline]) and [mathjaxinline]r[/mathjaxinline] is the radial distance from the axis of the cylinder. Calculate the electric field vector at any point in space outside the cylinder ([mathjaxinline]r&gt;a[/mathjaxinline]). Express your answer in terms of some or all of the following: [mathjaxinline]r[/mathjaxinline], [mathjaxinline]b[/mathjaxinline], [mathjaxinline]a[/mathjaxinline], pi for [mathjaxinline]\pi[/mathjaxinline], 'epsilon_0' for [mathjaxinline]\varepsilon _0[/mathjaxinline], 'hatr' for [mathjaxinline]\hat{\mathbf{r}}[/mathjaxinline], 'hattheta' for [mathjaxinline]\hat{\mathbf{\theta }}[/mathjaxinline], 'hatk' for [mathjaxinline]\hat{\mathbf{k}}[/mathjaxinline]. </p>
<p>
<p style="display:inline">[mathjaxinline]\vec{\mathbf{E}} =[/mathjaxinline]</p>
<div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_checkpoint_w3_6_2_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="unanswered inline">
<input type="text" name="input_checkpoint_w3_6_2_1" id="input_checkpoint_w3_6_2_1" aria-describedby="status_checkpoint_w3_6_2_1" value="" class="math" size="40"/>
<span class="trailing_text" id="trailing_text_checkpoint_w3_6_2_1"/>
<span class="status unanswered" id="status_checkpoint_w3_6_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_checkpoint_w3_6_2_1" class="answer"/>
<div id="display_checkpoint_w3_6_2_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_checkpoint_w3_6_2_1_dynamath" name="input_checkpoint_w3_6_2_1_dynamath"/>
</div>
</div></div>
</p>
<p>
<div class="solution-span">
<span id="solution_checkpoint_w3_6_solution_1"/>
</div></p>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Electric field of a non uniform charged cylinder." />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_checkpoint_w3_6" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_checkpoint_w3_6">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
<span class="problem-action-button-wrapper">
<button type="button" class="save problem-action-btn btn-default btn-small" data-value="Save">
<span class="icon fa fa-floppy-o" aria-hidden="true"></span>
<span aria-hidden="true">Save</span>
<span class="sr">Save your answer</span>
</button>
</span>
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w3_6-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w3_6-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w3_6-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="True">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="14942a64ea7411efb8100e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-L06bv04" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="vertical" data-init="VerticalStudentView" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-runtime-class="LmsRuntime">
<h2 class="hd hd-2 unit-title">L6bv4: Electric Field of a Sphere</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv04">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-request-token="14942a64ea7411efb8100e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv04" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="video" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">L06bv04: Electric Field of a Sphere</h3>
<div
id="video_L06bv04"
class="video closed"
data-metadata='{"saveStateUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv04/handler/xmodule_handler/save_user_state", "completionEnabled": false, "ytTestTimeout": 1500, "autohideHtml5": false, "completionPercentage": 0.95, "poster": null, "ytApiUrl": "https://www.youtube.com/iframe_api", "sources": [], "transcriptLanguages": {"en": "English"}, "saveStateEnabled": false, "captionDataDir": null, "recordedYoutubeIsAvailable": true, "autoAdvance": false, "duration": 0.0, "publishCompletionUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv04/handler/publish_completion", "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv04/handler/transcript/translation/__lang__", "prioritizeHls": false, "autoplay": false, "savedVideoPosition": 0.0, "streams": "1.00:pYVXiAWeQ4s", "speed": null, "generalSpeed": 1.0, "ytMetadataEndpoint": "", "showCaptions": "true", "start": 0.0, "transcriptLanguage": "en", "lmsRootURL": "https://openlearninglibrary.mit.edu", "end": 0.0, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv04/handler/transcript/available_translations"}'
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="L06bv04"></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_L06bv04">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L06bv04">
<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@L06bv04/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@L06bv04/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-request-token="14942a64ea7411efb8100e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-L6bQ10" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="vertical" data-init="VerticalStudentView" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-runtime-class="LmsRuntime">
<h2 class="hd hd-2 unit-title">L6bQ2: E-field Dependence on r</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w3_5">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="14942a64ea7411efb8100e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w3_5" data-graded="True" data-has-score="True" data-runtime-version="1" data-block-type="problem" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_checkpoint_w3_5" class="problems-wrapper" role="group"
aria-labelledby="checkpoint_w3_5-problem-title"
data-problem-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w3_5" data-url="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w3_5/handler/xmodule_handler"
data-problem-score="0.0"
data-problem-total-possible="2.0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="checkpoint_w3_5-problem-title" aria-describedby="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w3_5-problem-progress" tabindex="-1">
How Electric Field Falls Off with Distance from a Distribution
</h3>
<div class="problem-progress" id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w3_5-problem-progress"></div>
<div class="problem">
<div>
<center>
<img src="/assets/courseware/v1/4627153702d016e5ddb06f37451c066b/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w3_5b.svg" width="880"/>
</center>
<p>
Consider point [mathjaxinline]P[/mathjaxinline] a distance [mathjaxinline]d[/mathjaxinline] from the distributions of charges indicated in the figure above, how does the electric field fall off? For example, the magnitude of the electric field of a point charge a distance [mathjaxinline]d[/mathjaxinline] from the point charge falls off as [mathjaxinline]|\vec{E}| \propto \dfrac {1}{d^2}[/mathjaxinline]. Express your answer in terms of [mathjaxinline]d[/mathjaxinline]. If the field is uniform (i.e. independent of the value of [mathjaxinline]d[/mathjaxinline]) enter [mathjaxinline]c[/mathjaxinline]. </p>
<p><b class="bfseries">Figure 1</b>. Consider the infinite cylinder with a volume charge density [mathjaxinline]\rho (r)[/mathjaxinline]. The magnitude of the electric field at a point P outside the cylinder a distance [mathjaxinline]d[/mathjaxinline] from the axis of the cylinder falls off as: </p>
<p>
<p style="display:inline">[mathjaxinline]|\vec{E}|\propto[/mathjaxinline] </p>
<div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_checkpoint_w3_5_2_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="unanswered inline">
<input type="text" name="input_checkpoint_w3_5_2_1" id="input_checkpoint_w3_5_2_1" aria-describedby="status_checkpoint_w3_5_2_1" value="" class="math" size="20"/>
<span class="trailing_text" id="trailing_text_checkpoint_w3_5_2_1"/>
<span class="status unanswered" id="status_checkpoint_w3_5_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_checkpoint_w3_5_2_1" class="answer"/>
<div id="display_checkpoint_w3_5_2_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_checkpoint_w3_5_2_1_dynamath" name="input_checkpoint_w3_5_2_1_dynamath"/>
</div>
</div></div>
</p>
<p>
<div class="solution-span">
<span id="solution_checkpoint_w3_5_solution_1"/>
</div></p>
<p><b class="bfseries">Figure 2</b>. Consider the infinite slab of thickness [mathjaxinline]w[/mathjaxinline] with a volume charge density [mathjaxinline]\rho (x)[/mathjaxinline]. The magnitude of the electric field at a point P a distance [mathjaxinline]d[/mathjaxinline] from the right surface of the slab falls off as </p>
<p>
<p style="display:inline">[mathjaxinline]|\vec{E}|\propto[/mathjaxinline] </p>
<div class="inline" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_checkpoint_w3_5_3_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="unanswered inline">
<input type="text" name="input_checkpoint_w3_5_3_1" id="input_checkpoint_w3_5_3_1" aria-describedby="status_checkpoint_w3_5_3_1" value="" class="math" size="20"/>
<span class="trailing_text" id="trailing_text_checkpoint_w3_5_3_1"/>
<span class="status unanswered" id="status_checkpoint_w3_5_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_checkpoint_w3_5_3_1" class="answer"/>
<div id="display_checkpoint_w3_5_3_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_checkpoint_w3_5_3_1_dynamath" name="input_checkpoint_w3_5_3_1_dynamath"/>
</div>
</div></div>
</p>
<p>
<div class="solution-span">
<span id="solution_checkpoint_w3_5_solution_2"/>
</div></p>
<p><b class="bfseries">Figure 3</b>. Consider a positive and a negative charge separated by a distance [mathjaxinline]2a[/mathjaxinline]. The magnitude of the electric field at a point P a distance [mathjaxinline]d&gt;&gt;a[/mathjaxinline] from the center of the dipole (in order to show the details of the dipole in the figure, the distance [mathjaxinline]d&gt;&gt;a[/mathjaxinline] is not shown to scale) falls off as: </p>
<p>
<p style="display:inline">[mathjaxinline]|\vec{E}|\propto[/mathjaxinline] </p>
<div class="inline" tabindex="-1" aria-label="Question 3" role="group"><div id="inputtype_checkpoint_w3_5_4_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="unanswered inline">
<input type="text" name="input_checkpoint_w3_5_4_1" id="input_checkpoint_w3_5_4_1" aria-describedby="status_checkpoint_w3_5_4_1" value="" class="math" size="20"/>
<span class="trailing_text" id="trailing_text_checkpoint_w3_5_4_1"/>
<span class="status unanswered" id="status_checkpoint_w3_5_4_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_checkpoint_w3_5_4_1" class="answer"/>
<div id="display_checkpoint_w3_5_4_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_checkpoint_w3_5_4_1_dynamath" name="input_checkpoint_w3_5_4_1_dynamath"/>
</div>
</div></div>
</p>
<p>
<div class="solution-span">
<span id="solution_checkpoint_w3_5_solution_3"/>
</div></p>
<p><b class="bfseries">Figure 4</b>. Consider a sphere of radius [mathjaxinline]a[/mathjaxinline] with a volume charge density [mathjaxinline]\rho (r)[/mathjaxinline]. The magnitude of the electric field at a point P outside the sphere, a distance [mathjaxinline]d[/mathjaxinline] from the center of the sphere falls off as: </p>
<p>
<p style="display:inline">[mathjaxinline]|\vec{E}|\propto[/mathjaxinline] </p>
<div class="inline" tabindex="-1" aria-label="Question 4" role="group"><div id="inputtype_checkpoint_w3_5_5_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="unanswered inline">
<input type="text" name="input_checkpoint_w3_5_5_1" id="input_checkpoint_w3_5_5_1" aria-describedby="status_checkpoint_w3_5_5_1" value="" class="math" size="40"/>
<span class="trailing_text" id="trailing_text_checkpoint_w3_5_5_1"/>
<span class="status unanswered" id="status_checkpoint_w3_5_5_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_checkpoint_w3_5_5_1" class="answer"/>
<div id="display_checkpoint_w3_5_5_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_checkpoint_w3_5_5_1_dynamath" name="input_checkpoint_w3_5_5_1_dynamath"/>
</div>
</div></div>
</p>
<p>
<div class="solution-span">
<span id="solution_checkpoint_w3_5_solution_4"/>
</div></p>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="How Electric Field Falls Off with Distance from a Distribution" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_checkpoint_w3_5" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_checkpoint_w3_5">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
<span class="problem-action-button-wrapper">
<button type="button" class="save problem-action-btn btn-default btn-small" data-value="Save">
<span class="icon fa fa-floppy-o" aria-hidden="true"></span>
<span aria-hidden="true">Save</span>
<span class="sr">Save your answer</span>
</button>
</span>
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w3_5-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w3_5-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w3_5-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="True">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="14942a64ea7411efb8100e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-L06bv05" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="vertical" data-init="VerticalStudentView" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-runtime-class="LmsRuntime">
<h2 class="hd hd-2 unit-title">L6bv5: Electric Field Inside a Spherical Shell</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv05">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-request-token="14942a64ea7411efb8100e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv05" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="video" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">L06bv05: Electric Field Inside a Spherical Shell</h3>
<div
id="video_L06bv05"
class="video closed"
data-metadata='{"saveStateUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv05/handler/xmodule_handler/save_user_state", "completionEnabled": false, "ytTestTimeout": 1500, "autohideHtml5": false, "completionPercentage": 0.95, "poster": null, "ytApiUrl": "https://www.youtube.com/iframe_api", "sources": [], "transcriptLanguages": {"en": "English"}, "saveStateEnabled": false, "captionDataDir": null, "recordedYoutubeIsAvailable": true, "autoAdvance": false, "duration": 0.0, "publishCompletionUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv05/handler/publish_completion", "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv05/handler/transcript/translation/__lang__", "prioritizeHls": false, "autoplay": false, "savedVideoPosition": 0.0, "streams": "1.00:0Y2A8bfvdCI", "speed": null, "generalSpeed": 1.0, "ytMetadataEndpoint": "", "showCaptions": "true", "start": 0.0, "transcriptLanguage": "en", "lmsRootURL": "https://openlearninglibrary.mit.edu", "end": 0.0, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv05/handler/transcript/available_translations"}'
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="L06bv05"></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_L06bv05">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L06bv05">
<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@L06bv05/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@L06bv05/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-request-token="14942a64ea7411efb8100e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-cp_w2_8" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="vertical" data-init="VerticalStudentView" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-runtime-class="LmsRuntime">
<h2 class="hd hd-2 unit-title">L6bQ3: Spherical Shell</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w2_8">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="14942a64ea7411efb8100e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w2_8" data-graded="True" data-has-score="True" data-runtime-version="1" data-block-type="problem" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_checkpoint_w2_8" class="problems-wrapper" role="group"
aria-labelledby="checkpoint_w2_8-problem-title"
data-problem-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w2_8" data-url="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w2_8/handler/xmodule_handler"
data-problem-score="0.0"
data-problem-total-possible="1.0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="checkpoint_w2_8-problem-title" aria-describedby="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w2_8-problem-progress" tabindex="-1">
Spherical Shell
</h3>
<div class="problem-progress" id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w2_8-problem-progress"></div>
<div class="problem">
<div>
<p>
One can use Gauss's Law to show that the electric field at a radius located inside a solid sphere with a uniform charge density of charge grows linearly with distance from the center of the sphere. Inside a charged spherical shell ([mathjaxinline]r&lt;a[/mathjaxinline], where [mathjaxinline]a[/mathjaxinline] is the inner radius of the shell), which expression best describes the magnitude of the electric field? </p>
<center>
<img src="/assets/courseware/v1/a8c287f1d3064219fb7590e63522fa02/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w2_8_1.svg" width="330"/>
</center>
<p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_checkpoint_w2_8_2_1">
<fieldset aria-describedby="status_checkpoint_w2_8_2_1">
<div class="field">
<input type="radio" name="input_checkpoint_w2_8_2_1" id="input_checkpoint_w2_8_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="checkpoint_w2_8_2_1-choice_1-label" for="input_checkpoint_w2_8_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w2_8_2_1">
<text> Zero</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_checkpoint_w2_8_2_1" id="input_checkpoint_w2_8_2_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="checkpoint_w2_8_2_1-choice_2-label" for="input_checkpoint_w2_8_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w2_8_2_1">
<text> Uniform but non-zero</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_checkpoint_w2_8_2_1" id="input_checkpoint_w2_8_2_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="checkpoint_w2_8_2_1-choice_3-label" for="input_checkpoint_w2_8_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w2_8_2_1">
<text> Still grows linearly with [mathjaxinline]r[/mathjaxinline]</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_checkpoint_w2_8_2_1" id="input_checkpoint_w2_8_2_1_choice_4" class="field-input input-radio" value="choice_4"/><label id="checkpoint_w2_8_2_1-choice_4-label" for="input_checkpoint_w2_8_2_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w2_8_2_1">
<text> Some other functional form of [mathjaxinline]r[/mathjaxinline] (use Gauss's Law)</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_checkpoint_w2_8_2_1" id="input_checkpoint_w2_8_2_1_choice_5" class="field-input input-radio" value="choice_5"/><label id="checkpoint_w2_8_2_1-choice_5-label" for="input_checkpoint_w2_8_2_1_choice_5" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w2_8_2_1">
<text> Can't determine with Gauss's Law</text>
</label>
</div>
<span id="answer_checkpoint_w2_8_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_checkpoint_w2_8_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
</p>
<p>
<div class="solution-span">
<span id="solution_checkpoint_w2_8_solution_1"/>
</div></p>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Spherical Shell" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_checkpoint_w2_8" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_checkpoint_w2_8">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
<span class="problem-action-button-wrapper">
<button type="button" class="save problem-action-btn btn-default btn-small" data-value="Save">
<span class="icon fa fa-floppy-o" aria-hidden="true"></span>
<span aria-hidden="true">Save</span>
<span class="sr">Save your answer</span>
</button>
</span>
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w2_8-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w2_8-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w2_8-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="True">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="14942a64ea7411efb8100e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-L06bv06" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="vertical" data-init="VerticalStudentView" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-runtime-class="LmsRuntime">
<h2 class="hd hd-2 unit-title">L6bv6: Force on a Charge Inside a Spherical Shell</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv06">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-request-token="14942a64ea7411efb8100e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv06" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="video" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">L06bv06: Force on a Charge Inside a Spherical Shell</h3>
<div
id="video_L06bv06"
class="video closed"
data-metadata='{"saveStateUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv06/handler/xmodule_handler/save_user_state", "completionEnabled": false, "ytTestTimeout": 1500, "autohideHtml5": false, "completionPercentage": 0.95, "poster": null, "ytApiUrl": "https://www.youtube.com/iframe_api", "sources": [], "transcriptLanguages": {"en": "English"}, "saveStateEnabled": false, "captionDataDir": null, "recordedYoutubeIsAvailable": true, "autoAdvance": false, "duration": 0.0, "publishCompletionUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv06/handler/publish_completion", "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv06/handler/transcript/translation/__lang__", "prioritizeHls": false, "autoplay": false, "savedVideoPosition": 0.0, "streams": "1.00:7fmW2-szpxY", "speed": null, "generalSpeed": 1.0, "ytMetadataEndpoint": "", "showCaptions": "true", "start": 0.0, "transcriptLanguage": "en", "lmsRootURL": "https://openlearninglibrary.mit.edu", "end": 0.0, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv06/handler/transcript/available_translations"}'
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="L06bv06"></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_L06bv06">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L06bv06">
<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@L06bv06/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@L06bv06/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-request-token="14942a64ea7411efb8100e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-L06bv07" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="vertical" data-init="VerticalStudentView" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-runtime-class="LmsRuntime">
<h2 class="hd hd-2 unit-title">L6bv7: Electric Field of Two Spherical Shells</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv07">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-request-token="14942a64ea7411efb8100e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv07" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="video" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+8.02.1x+1T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">L06bv07: Electric Field of Two Spherical Shells</h3>
<div
id="video_L06bv07"
class="video closed"
data-metadata='{"saveStateUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv07/handler/xmodule_handler/save_user_state", "completionEnabled": false, "ytTestTimeout": 1500, "autohideHtml5": false, "completionPercentage": 0.95, "poster": null, "ytApiUrl": "https://www.youtube.com/iframe_api", "sources": [], "transcriptLanguages": {"en": "English"}, "saveStateEnabled": false, "captionDataDir": null, "recordedYoutubeIsAvailable": true, "autoAdvance": false, "duration": 0.0, "publishCompletionUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv07/handler/publish_completion", "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv07/handler/transcript/translation/__lang__", "prioritizeHls": false, "autoplay": false, "savedVideoPosition": 0.0, "streams": "1.00:wY-gJf2YIPk", "speed": null, "generalSpeed": 1.0, "ytMetadataEndpoint": "", "showCaptions": "true", "start": 0.0, "transcriptLanguage": "en", "lmsRootURL": "https://openlearninglibrary.mit.edu", "end": 0.0, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L06bv07/handler/transcript/available_translations"}'
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="L06bv07"></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_L06bv07">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L06bv07">
<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@L06bv07/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@L06bv07/handler/transcript/download" data-value="txt">Download Text (.txt) file</a>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
© All Rights Reserved