<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-lesson02-Efields" 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-mathrev3-v1">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-request-token="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@html+block@html-mathrev3-v1" 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>In this lesson, we transition to thinking about the elctric fields that are produced by electric charges.</p><p> Textbook Links </p><ul><li> Chapter 1: Fields <a href="/courses/course-v1:MITx+8.02.1x+1T2019/pdfbook/0/chapter/1/3"><i class="it">chapter 1</i></a></li><li> Chapter 2: Coulomb's Law <a href="/courses/course-v1:MITx+8.02.1x+1T2019/pdfbook/0/chapter/2/7"><i class="it">chapter 2, sections 3-6</i></a></li></ul>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-L02v01" 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">L2v1: Vector Fields</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L02v01">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-request-token="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L02v01" 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">L02v01: Vector Fields</h3>
<div
id="video_L02v01"
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@L02v01/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@L02v01/handler/publish_completion", "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L02v01/handler/transcript/translation/__lang__", "prioritizeHls": false, "autoplay": false, "savedVideoPosition": 0.0, "streams": "1.00:Rb3bf7bc_8c", "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@L02v01/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="L02v01"></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_L02v01">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L02v01">
<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@L02v01/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@L02v01/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="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-L02v02" 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">L2v2: Kinds of Vector Fields</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L02v02">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-request-token="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L02v02" 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">L02v02: Kinds of Vector Fields</h3>
<div
id="video_L02v02"
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@L02v02/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@L02v02/handler/publish_completion", "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L02v02/handler/transcript/translation/__lang__", "prioritizeHls": false, "autoplay": false, "savedVideoPosition": 0.0, "streams": "1.00:xrTkRGYBMKw", "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@L02v02/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="L02v02"></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_L02v02">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L02v02">
<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@L02v02/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@L02v02/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="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-L02v03" 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">L2v3: Electric Field of a Positive Point Charge</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L02v03">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-request-token="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L02v03" 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">L02v03: Electric FIeld of a Positive Point Charge</h3>
<div
id="video_L02v03"
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@L02v03/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@L02v03/handler/publish_completion", "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L02v03/handler/transcript/translation/__lang__", "prioritizeHls": false, "autoplay": false, "savedVideoPosition": 0.0, "streams": "1.00:Fraxulexur0", "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@L02v03/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="L02v03"></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_L02v03">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L02v03">
<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@L02v03/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@L02v03/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="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-html-lesson02_01" 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">Electric Field of a Point Charge Summary.</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@html+block@lesson02_01">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-request-token="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@html+block@lesson02_01" 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><b>Electric field due to a point charge. </b></p><p>Consider an isolated point-like object of charge \(q_s\) to be the only source of electric field. The electric field vector produced by the charge at a given point \(P\), a distance \(r_{S,P}\) from the charge, is given by:</p><p>\[\displaystyle \vec{E} = k\frac{q_s}{r_{S,P}^2}\hat{r}_{S,P}\]</p><p>where \(\hat{r}_{S,P}\) is a unit vector in the direction of the
line from the charge \(q_s\) to the point \(P\). The direction of this unit vector is shown in the figure below. </p><p><center><img src="/assets/courseware/v1/ba8848fbad5f8fcac569a224702c2897/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_html_lesson2_E_point_charge.svg" width="300"/></center></p><p><b>Magnitude of the Electric field.</b></p><p>From the relationship of the electric field to Coulomb's Law, we find that the <i>magnitude</i> of the electric field is proportional to the <i>magnitude</i> of the charge, and inversely proportional to the square of the distance between the point source and the field point:</p><p>\[|\vec{E}| \propto \frac{|q_s|}{r_{S,P}^2} \] </p><p>Finally, we need a constant to get the size and units of the electric field correct. One way of writing this constant is shown below. A different way of writing this constant (related to Gauss' Law) will be discussed later in the course.
</p><p>\[|\vec{E}|= k_e \frac{|q_s|}{r_{S,P}^2} \] </p><p><b>Direction of the Electric field.</b></p><p>The electric field is parallel to \(\hat{r}_{S,P}\). It points away from a positive charge (left figure) and towards a negative charge (right figure).</p><p><center><img src="/assets/courseware/v1/ff0d7e12f368e34f53655cdffee2b12b/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_html_lesson2_E_point_charge_2.svg" width="700"/></center></p><p>Putting it all together:
</p><p>\[\vec{E} = k_e \frac{q_s}{r_{S,P}^2}\hat{r}_{S,P} \] </p><p>Notice that if \(q_s \gt 0\), the field points in the same direction as \(\hat{r}_{S,P}\) (as expected from the left figure above), while if \(q_s\lt 0\), the field points in the \(-\hat{r}_{S,P}\) direction (right figure).</p><p><b>Calculating Force from the Electric field.</b></p><p>If we have a charge \(q\) in an electric field, it will feel a force due to that field. To find the force, we just multiply the charge by the electric field:</p><p>\[\displaystyle \vec{F} = q\vec{E}\]</p>
One can also think of this force as arising from the interactions with the charge or charges that are the source of the electric field, but attributing the force as being due to the field itself is more accurate.
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-checkpoint_w1_10" 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">L2Q1: Rewriting the Electric Field of a Point Charge.</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_10">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_10" 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_w1_10" class="problems-wrapper" role="group"
aria-labelledby="checkpoint_w1_10-problem-title"
data-problem-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_10" data-url="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_10/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_w1_10-problem-title" aria-describedby="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_10-problem-progress" tabindex="-1">
Rewriting the electric field of a point charge, Part 1.
</h3>
<div class="problem-progress" id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_10-problem-progress"></div>
<div class="problem">
<div>
<span>
<p>
<b class="bfseries">Part 1. Electric Field of a point charge at the origin.</b>
</p>
<center>
<img src="/assets/courseware/v1/6ad40d24f9ead9970f8372bf271231b4/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_10.svg" width="330"/>
</center>
<p>
Consider a point-like object of charge [mathjaxinline]q_S[/mathjaxinline] at the origin of the coordinate system shown in the figure. The electric field at a point [mathjaxinline]P[/mathjaxinline] a distance [mathjaxinline]r_{S,P}[/mathjaxinline] from the charge is given by: </p>
<table id="a0000000002" cellpadding="7" width="100%" cellspacing="0" class="eqnarray" style="table-layout:auto">
<tr id="a0000000003">
<td style="width:40%; border:none">&#160;</td>
<td style="vertical-align:middle; text-align:right; border:none">
[mathjaxinline]\displaystyle \displaystyle \vec{E} = kq_S\frac{\hat{r}_{S,P}}{r_{S,P}^2}[/mathjaxinline]
</td>
<td style="width:40%; border:none">&#160;</td>
<td style="width:20%; border:none" class="eqnnum">
<span>(<span>1</span>)</span>
</td>
</tr>
</table>
<p>
where [mathjaxinline]\hat{r}_{S,P}[/mathjaxinline] is the unit vector along the line joining the charge and the point [mathjaxinline]P[/mathjaxinline] and directed from [mathjaxinline]q_S[/mathjaxinline] to point [mathjaxinline]P[/mathjaxinline]. Let [mathjaxinline]\vec{r}_{S,P}[/mathjaxinline], be the position vector of point [mathjaxinline]P[/mathjaxinline] measured from the origin of the coordinate system. Drag and drop the proper terms to obtain an alternative expression of the electric field that does not contain [mathjaxinline]\hat{r}_{S,P}[/mathjaxinline]. </p>
<p>
' <span><div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_checkpoint_w1_10_2_1" class="capa_inputtype">
<div class="drag_and_drop_problem_div" id="drag_and_drop_div_checkpoint_w1_10_2_1" data-plain-id="checkpoint_w1_10_2_1">
</div>
<div class="drag_and_drop_problem_json" id="drag_and_drop_json_checkpoint_w1_10_2_1" style="display:none;">{"target_outline": "false", "draggables": [{"target_fields": [], "can_reuse": "true", "icon": "/assets/courseware/v1/7c76370f1ea159ce5551e60840b3253d/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_10_dnd_checkpoint_w1_10_dnd_dnd_label1.png", "label": "", "id": "A"}, {"target_fields": [], "can_reuse": "true", "icon": "/assets/courseware/v1/fcc8817b65fe3581b8fb4ded36ebca2b/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_10_dnd_checkpoint_w1_10_dnd_dnd_label2.png", "label": "", "id": "B"}, {"target_fields": [], "can_reuse": "true", "icon": "/assets/courseware/v1/de7f144e1da3ffdfe5537b5212ede88e/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_10_dnd_checkpoint_w1_10_dnd_dnd_label3.png", "label": "", "id": "C"}, {"target_fields": [], "can_reuse": "true", "icon": "/assets/courseware/v1/7423ad9c414cc66bacab7542a9fee225/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_10_dnd_checkpoint_w1_10_dnd_dnd_label4.png", "label": "", "id": "D"}, {"target_fields": [], "can_reuse": "true", "icon": "/assets/courseware/v1/c88aa2680d72b4ffcc29daad2d528ab4/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_10_dnd_checkpoint_w1_10_dnd_dnd_label5.png", "label": "", "id": "E"}], "label_bg_color": "rgb(222, 139, 238)", "one_per_target": "true", "targets": [{"y": "67", "id": "1", "h": "61", "w": "65", "x": "60"}, {"y": "67", "id": "2", "h": "61", "w": "65", "x": "142"}, {"y": "33", "id": "3", "h": "61", "w": "65", "x": "226"}, {"y": "113", "id": "4", "h": "61", "w": "65", "x": "226"}], "base_image": "/assets/courseware/v1/cb4806d517ce0c5da68ae8d52adc47d7/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_10_dnd_checkpoint_w1_10_dnd_dnd.png"}</div>
<div class="script_placeholder" data-src="/static/js/capa/drag_and_drop.a31124208b9b.js"/>
<div class="unanswered" id="status_checkpoint_w1_10_2_1">
<input type="text" name="input_checkpoint_w1_10_2_1" id="input_checkpoint_w1_10_2_1" aria-describedby="answer_checkpoint_w1_10_2_1" value="" style="display:none;"/>
<p class="indicator-container drag-and-drop--status" aria-describedby="input_checkpoint_w1_10_2_1">
<span class="status unanswered" id="status_checkpoint_w1_10_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</p>
<p id="answer_checkpoint_w1_10_2_1" class="answer"/>
</div>
</div></div><div class="solution-span">
<span id="solution_checkpoint_w1_10_solution_1"/>
</div></span></p>
<p>
<div class="solution-span">
<span id="solution_checkpoint_w1_10_solution_2"/>
</div></p>
</span>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Rewriting the electric field of a point charge, Part 1." />
<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_w1_10" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_checkpoint_w1_10">
<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_w1_10-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_w1_10-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_w1_10-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 class="vert vert-1" data-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_10_2">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_10_2" 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_w1_10_2" class="problems-wrapper" role="group"
aria-labelledby="checkpoint_w1_10_2-problem-title"
data-problem-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_10_2" data-url="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_10_2/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_w1_10_2-problem-title" aria-describedby="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_10_2-problem-progress" tabindex="-1">
Rewriting the electric field of a point charge, Part 2.
</h3>
<div class="problem-progress" id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_10_2-problem-progress"></div>
<div class="problem">
<div>
<span>
<p>
<b class="bfseries">Part 2. Electric Field of a point away from the origin.</b>
</p>
<center>
<img src="/assets/courseware/v1/717f29d19d644c0e96776909c88fd416/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_10_2.svg" width="330"/>
</center>
<p>
The coordinate system of part 1 is now shifted so that the point charge is at a position [mathjaxinline]\vec{r}_ S[/mathjaxinline], and point [mathjaxinline]P[/mathjaxinline] is at position [mathjaxinline]\vec{r}_ P[/mathjaxinline] as shown in the figure above. These two vectors are measured with respect to the new origin. </p>
<p>
Drag and drop the proper terms to express the electric field at point [mathjaxinline]P[/mathjaxinline] in the coordinate system shown in the figure. </p>
<span>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_checkpoint_w1_10_2_2_1" class="capa_inputtype">
<div class="drag_and_drop_problem_div" id="drag_and_drop_div_checkpoint_w1_10_2_2_1" data-plain-id="checkpoint_w1_10_2_2_1">
</div>
<div class="drag_and_drop_problem_json" id="drag_and_drop_json_checkpoint_w1_10_2_2_1" style="display:none;">{"target_outline": "false", "draggables": [{"target_fields": [], "can_reuse": "true", "icon": "/assets/courseware/v1/e69685b41c30d665c7c6df9c91140d1f/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_10_2_dnd_checkpoint_w1_10_2_dnd_dnd_label1.png", "label": "", "id": "A"}, {"target_fields": [], "can_reuse": "true", "icon": "/assets/courseware/v1/c21e28bc8e27b1c01eeb6fdb6442a588/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_10_2_dnd_checkpoint_w1_10_2_dnd_dnd_label2.png", "label": "", "id": "B"}, {"target_fields": [], "can_reuse": "true", "icon": "/assets/courseware/v1/70bdbc4252c392e9cd46f34289c84755/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_10_2_dnd_checkpoint_w1_10_2_dnd_dnd_label3.png", "label": "", "id": "C"}, {"target_fields": [], "can_reuse": "true", "icon": "/assets/courseware/v1/196e5b592316eed3ddd656f9abb4b913/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_10_2_dnd_checkpoint_w1_10_2_dnd_dnd_label4.png", "label": "", "id": "D"}, {"target_fields": [], "can_reuse": "true", "icon": "/assets/courseware/v1/481d9368596dfead232e14c7a66050e2/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_10_2_dnd_checkpoint_w1_10_2_dnd_dnd_label5.png", "label": "", "id": "E"}, {"target_fields": [], "can_reuse": "true", "icon": "/assets/courseware/v1/ee04e2458e56de2dd18d8227c91fe78d/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_10_2_dnd_checkpoint_w1_10_2_dnd_dnd_label6.png", "label": "", "id": "F"}, {"target_fields": [], "can_reuse": "true", "icon": "/assets/courseware/v1/f136a4d00e4a72136aa8aaa86df43869/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_10_2_dnd_checkpoint_w1_10_2_dnd_dnd_label7.png", "label": "", "id": "G"}, {"target_fields": [], "can_reuse": "true", "icon": "/assets/courseware/v1/bc06233a64f21ad1f09d10c49fee785d/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_10_2_dnd_checkpoint_w1_10_2_dnd_dnd_label8.png", "label": "", "id": "H"}, {"target_fields": [], "can_reuse": "true", "icon": "/assets/courseware/v1/0df0e3149cf4b2a746b65fbb0f7ab7eb/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_10_2_dnd_checkpoint_w1_10_2_dnd_dnd_label9.png", "label": "", "id": "I"}], "label_bg_color": "rgb(222, 139, 238)", "one_per_target": "true", "targets": [{"y": "66", "id": "1", "h": "61", "w": "108", "x": "60"}, {"y": "66", "id": "2", "h": "61", "w": "107", "x": "185"}, {"y": "32", "id": "3", "h": "61", "w": "107", "x": "313"}, {"y": "113", "id": "4", "h": "61", "w": "107", "x": "313"}], "base_image": "/assets/courseware/v1/9c029ad01c15917d924643675777e52d/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_10_2_dnd_checkpoint_w1_10_2_dnd_dnd.png"}</div>
<div class="script_placeholder" data-src="/static/js/capa/drag_and_drop.a31124208b9b.js"/>
<div class="unanswered" id="status_checkpoint_w1_10_2_2_1">
<input type="text" name="input_checkpoint_w1_10_2_2_1" id="input_checkpoint_w1_10_2_2_1" aria-describedby="answer_checkpoint_w1_10_2_2_1" value="" style="display:none;"/>
<p class="indicator-container drag-and-drop--status" aria-describedby="input_checkpoint_w1_10_2_2_1">
<span class="status unanswered" id="status_checkpoint_w1_10_2_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</p>
<p id="answer_checkpoint_w1_10_2_2_1" class="answer"/>
</div>
</div></div>
<div class="solution-span">
<span id="solution_checkpoint_w1_10_2_solution_1"/>
</div></span>
<p>
<div class="solution-span">
<span id="solution_checkpoint_w1_10_2_solution_2"/>
</div></p>
</span>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Rewriting the electric field of a point charge, Part 2." />
<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_w1_10_2" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_checkpoint_w1_10_2">
<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_w1_10_2-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_w1_10_2-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_w1_10_2-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="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-checkpoint_w1_17" 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">L2Q2: Force on a Charge from an Electric Field</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_17">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_17" 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_w1_17" class="problems-wrapper" role="group"
aria-labelledby="checkpoint_w1_17-problem-title"
data-problem-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_17" data-url="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_17/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_w1_17-problem-title" aria-describedby="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_17-problem-progress" tabindex="-1">
Two charges in a uniform field.
</h3>
<div class="problem-progress" id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_17-problem-progress"></div>
<div class="problem">
<div>
<center>
<img src="/assets/courseware/v1/7cba09b01c9cebba138502a64cfa0aa9/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_17_2.svg" width="440"/>
</center>
<p>
Consider a uniform electric field of magnitude [mathjaxinline]E_0[/mathjaxinline] pointing in the [mathjaxinline]+\hat{i}[/mathjaxinline] direction. At the instant illustrated in the figure, object 1 with charge [mathjaxinline]q_1=q[/mathjaxinline] (where [mathjaxinline]q&gt;0[/mathjaxinline])is moving with speed [mathjaxinline]v_1[/mathjaxinline] in the direction shown, and object 2 of charge [mathjaxinline]q_2=-3q[/mathjaxinline] is at rest. Note that the two charges will exert forces on each other, but you will not be asked about that in this problem. Express your answer in terms of [mathjaxinline]q[/mathjaxinline], E_0 for [mathjaxinline]E_0[/mathjaxinline], v_1 for [mathjaxinline]v_1[/mathjaxinline], hati for [mathjaxinline]\hat{i}[/mathjaxinline], and hatj for [mathjaxinline]\hat{j}[/mathjaxinline] as needed. </p>
<p><b class="bfseries">(Part a)</b> What is [mathjaxinline]\vec{F}_1[/mathjaxinline], the force exerted by the electric field [mathjaxinline]E_0[/mathjaxinline] on object 1? </p>
<p>
<p style="display:inline">[mathjaxinline]\vec{F}_1=[/mathjaxinline]</p>
<div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_checkpoint_w1_17_2_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="unanswered inline">
<input type="text" name="input_checkpoint_w1_17_2_1" id="input_checkpoint_w1_17_2_1" aria-describedby="status_checkpoint_w1_17_2_1" value="" class="math" size="25"/>
<span class="trailing_text" id="trailing_text_checkpoint_w1_17_2_1"/>
<span class="status unanswered" id="status_checkpoint_w1_17_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_checkpoint_w1_17_2_1" class="answer"/>
<div id="display_checkpoint_w1_17_2_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_checkpoint_w1_17_2_1_dynamath" name="input_checkpoint_w1_17_2_1_dynamath"/>
</div>
</div></div>
</p>
<p><b class="bfseries">(Part b)</b> What is [mathjaxinline]\vec{F}_2[/mathjaxinline], the force exerted by the electric field [mathjaxinline]E_0[/mathjaxinline] on object 2? </p>
<p>
<p style="display:inline">[mathjaxinline]\vec{F}_2=[/mathjaxinline]</p>
<div class="inline" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_checkpoint_w1_17_3_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="unanswered inline">
<input type="text" name="input_checkpoint_w1_17_3_1" id="input_checkpoint_w1_17_3_1" aria-describedby="status_checkpoint_w1_17_3_1" value="" class="math" size="25"/>
<span class="trailing_text" id="trailing_text_checkpoint_w1_17_3_1"/>
<span class="status unanswered" id="status_checkpoint_w1_17_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_checkpoint_w1_17_3_1" class="answer"/>
<div id="display_checkpoint_w1_17_3_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_checkpoint_w1_17_3_1_dynamath" name="input_checkpoint_w1_17_3_1_dynamath"/>
</div>
</div></div>
</p>
<p>
<div class="solution-span">
<span id="solution_checkpoint_w1_17_solution_1"/>
</div></p>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Two charges in a uniform field." />
<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_w1_17" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_checkpoint_w1_17">
<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_w1_17-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_w1_17-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_w1_17-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="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-L02v04" 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">L2v4: Superposition</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L02v04">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-request-token="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L02v04" 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">L02v04: Superposition</h3>
<div
id="video_L02v04"
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@L02v04/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@L02v04/handler/publish_completion", "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L02v04/handler/transcript/translation/__lang__", "prioritizeHls": false, "autoplay": false, "savedVideoPosition": 0.0, "streams": "1.00:E6IOxi_mWA8", "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@L02v04/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="L02v04"></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_L02v04">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L02v04">
<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@L02v04/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@L02v04/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="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-lesson02-checkpoint_w1_1" 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">L2Q3: Equal 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_1a">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_1a" 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_w1_1a" class="problems-wrapper" role="group"
aria-labelledby="checkpoint_w1_1a-problem-title"
data-problem-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_1a" data-url="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_1a/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_w1_1a-problem-title" aria-describedby="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_1a-problem-progress" tabindex="-1">
Equal Charges, Part 1.
</h3>
<div class="problem-progress" id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_1a-problem-progress"></div>
<div class="problem">
<div>
<center>
<img src="/assets/courseware/v1/dd49c3fd14dbb08ed21abbd4052acc01/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_1_1a.svg" width="330"/>
</center>
<p>
Six equal positive charges [mathjaxinline]+Q[/mathjaxinline] sit at the vertices of a regular hexagon with sides of length R (note that R is also the distance from each charge to the center of the hexagon as shown). The electric field at the center of the hexagon (point [mathjaxinline]P[/mathjaxinline]) is given by (assume that [mathjaxinline]\hat{j}[/mathjaxinline] points up in the figure): </p>
<p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_checkpoint_w1_1a_2_1">
<fieldset aria-describedby="status_checkpoint_w1_1a_2_1">
<div class="field">
<input type="radio" name="input_checkpoint_w1_1a_2_1" id="input_checkpoint_w1_1a_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="checkpoint_w1_1a_2_1-choice_1-label" for="input_checkpoint_w1_1a_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w1_1a_2_1">
<text> [mathjaxinline]\vec{E}=\frac{2 k_ e Q}{R^2} \hat{j}[/mathjaxinline]</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_checkpoint_w1_1a_2_1" id="input_checkpoint_w1_1a_2_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="checkpoint_w1_1a_2_1-choice_2-label" for="input_checkpoint_w1_1a_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w1_1a_2_1">
<text> [mathjaxinline]\vec{E}=-\frac{2k_ e Q}{R^2} \hat{j}[/mathjaxinline]</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_checkpoint_w1_1a_2_1" id="input_checkpoint_w1_1a_2_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="checkpoint_w1_1a_2_1-choice_3-label" for="input_checkpoint_w1_1a_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w1_1a_2_1">
<text> [mathjaxinline]\vec{E}=\frac{k_ e Q}{R^2} \hat{j}[/mathjaxinline]</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_checkpoint_w1_1a_2_1" id="input_checkpoint_w1_1a_2_1_choice_4" class="field-input input-radio" value="choice_4"/><label id="checkpoint_w1_1a_2_1-choice_4-label" for="input_checkpoint_w1_1a_2_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w1_1a_2_1">
<text> [mathjaxinline]\vec{E}=-\frac{k_ e Q}{R^2} \hat{j}[/mathjaxinline]</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_checkpoint_w1_1a_2_1" id="input_checkpoint_w1_1a_2_1_choice_5" class="field-input input-radio" value="choice_5"/><label id="checkpoint_w1_1a_2_1-choice_5-label" for="input_checkpoint_w1_1a_2_1_choice_5" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w1_1a_2_1">
<text> [mathjaxinline]\vec{E}=0[/mathjaxinline]</text>
</label>
</div>
<span id="answer_checkpoint_w1_1a_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_checkpoint_w1_1a_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_w1_1a_solution_1"/>
</div></p>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Equal Charges, Part 1." />
<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_w1_1a" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_checkpoint_w1_1a">
<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_w1_1a-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_w1_1a-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_w1_1a-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 class="vert vert-1" data-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_1">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_1" 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_w1_1" class="problems-wrapper" role="group"
aria-labelledby="checkpoint_w1_1-problem-title"
data-problem-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_1" data-url="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_1/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_w1_1-problem-title" aria-describedby="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_1-problem-progress" tabindex="-1">
Equal Charges, Part 2.
</h3>
<div class="problem-progress" id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_1-problem-progress"></div>
<div class="problem">
<div>
<center>
<img src="/assets/courseware/v1/6187c6151cb65c3543230d271abd7e0d/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_1_1.svg" width="330"/>
</center>
<p>
We remove the bottom charge. The electric field at the center of the hexagon (point [mathjaxinline]P[/mathjaxinline]) is: </p>
<p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_checkpoint_w1_1_2_1">
<fieldset aria-describedby="status_checkpoint_w1_1_2_1">
<div class="field">
<input type="radio" name="input_checkpoint_w1_1_2_1" id="input_checkpoint_w1_1_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="checkpoint_w1_1_2_1-choice_1-label" for="input_checkpoint_w1_1_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w1_1_2_1">
<text> [mathjaxinline]\vec{E}=\frac{2 k_ e Q}{R^2} \hat{j}[/mathjaxinline]</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_checkpoint_w1_1_2_1" id="input_checkpoint_w1_1_2_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="checkpoint_w1_1_2_1-choice_2-label" for="input_checkpoint_w1_1_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w1_1_2_1">
<text> [mathjaxinline]\vec{E}=-\frac{2k_ e Q}{R^2} \hat{j}[/mathjaxinline]</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_checkpoint_w1_1_2_1" id="input_checkpoint_w1_1_2_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="checkpoint_w1_1_2_1-choice_3-label" for="input_checkpoint_w1_1_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w1_1_2_1">
<text> [mathjaxinline]\vec{E}=\frac{k_ e Q}{R^2} \hat{j}[/mathjaxinline]</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_checkpoint_w1_1_2_1" id="input_checkpoint_w1_1_2_1_choice_4" class="field-input input-radio" value="choice_4"/><label id="checkpoint_w1_1_2_1-choice_4-label" for="input_checkpoint_w1_1_2_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w1_1_2_1">
<text> [mathjaxinline]\vec{E}=-\frac{k_ e Q}{R^2} \hat{j}[/mathjaxinline]</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_checkpoint_w1_1_2_1" id="input_checkpoint_w1_1_2_1_choice_5" class="field-input input-radio" value="choice_5"/><label id="checkpoint_w1_1_2_1-choice_5-label" for="input_checkpoint_w1_1_2_1_choice_5" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w1_1_2_1">
<text> [mathjaxinline]\vec{E}=0[/mathjaxinline]</text>
</label>
</div>
<span id="answer_checkpoint_w1_1_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_checkpoint_w1_1_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_w1_1_solution_1"/>
</div></p>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Equal Charges, Part 2." />
<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_w1_1" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_checkpoint_w1_1">
<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_w1_1-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_w1_1-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_w1_1-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="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-L02v05" 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">L2v5: Worked Example - Total Electric Field Due to 2 Charges</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L02v05">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-request-token="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L02v05" 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">L02v05: Worked Example - Total Electric Field Due to 2 Charges</h3>
<div
id="video_L02v05"
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@L02v05/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@L02v05/handler/publish_completion", "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L02v05/handler/transcript/translation/__lang__", "prioritizeHls": false, "autoplay": false, "savedVideoPosition": 0.0, "streams": "1.00:WN_KgndSECY", "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@L02v05/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="L02v05"></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_L02v05">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L02v05">
<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@L02v05/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@L02v05/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="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-checkpoint_w1_16" 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">L2Q4: Electric Field due to 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_16">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_16" 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_w1_16" class="problems-wrapper" role="group"
aria-labelledby="checkpoint_w1_16-problem-title"
data-problem-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_16" data-url="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_16/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_w1_16-problem-title" aria-describedby="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_16-problem-progress" tabindex="-1">
Electric field produced by two charges.
</h3>
<div class="problem-progress" id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_16-problem-progress"></div>
<div class="problem">
<div>
<center>
<img src="/assets/courseware/v1/c8a8589d8220b8d4422d3881984e583d/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_16.svg" width="440"/>
</center>
<p>
Two objects of charges [mathjaxinline]+q[/mathjaxinline] and [mathjaxinline]-q[/mathjaxinline] are separated by a distance [mathjaxinline]a[/mathjaxinline]. Calculate the electric field at point [mathjaxinline]P[/mathjaxinline] located at a distance [mathjaxinline]d[/mathjaxinline] from the center point between the two charges. Express your answer in terms of [mathjaxinline]k[/mathjaxinline], [mathjaxinline]q[/mathjaxinline], [mathjaxinline]a[/mathjaxinline], [mathjaxinline]d[/mathjaxinline], hati for [mathjaxinline]\hat{i}[/mathjaxinline], and hatj for [mathjaxinline]\hat{j}[/mathjaxinline] as needed. </p>
<p>
<p style="display:inline">[mathjaxinline]\vec{E}=[/mathjaxinline]</p>
<div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_checkpoint_w1_16_2_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="unanswered inline">
<input type="text" name="input_checkpoint_w1_16_2_1" id="input_checkpoint_w1_16_2_1" aria-describedby="status_checkpoint_w1_16_2_1" value="" class="math" size="35"/>
<span class="trailing_text" id="trailing_text_checkpoint_w1_16_2_1"/>
<span class="status unanswered" id="status_checkpoint_w1_16_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_checkpoint_w1_16_2_1" class="answer"/>
<div id="display_checkpoint_w1_16_2_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_checkpoint_w1_16_2_1_dynamath" name="input_checkpoint_w1_16_2_1_dynamath"/>
</div>
</div></div>
</p>
<p>
<div class="solution-span">
<span id="solution_checkpoint_w1_16_solution_1"/>
</div></p>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Electric field produced by two charges." />
<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_w1_16" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_checkpoint_w1_16">
<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_w1_16-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_w1_16-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_w1_16-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="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-L02v06" 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">L02v06: Electric Field Lines</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L02v06">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-request-token="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@video+block@L02v06" 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">L02v06: Electric Field Lines</h3>
<div
id="video_L02v06"
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@L02v06/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@L02v06/handler/publish_completion", "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@video+block@L02v06/handler/transcript/translation/__lang__", "prioritizeHls": false, "autoplay": false, "savedVideoPosition": 0.0, "streams": "1.00:pb61-V_rY0U", "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@L02v06/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="L02v06"></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_L02v06">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L02v06">
<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@L02v06/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@L02v06/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="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-pcq-w2d1a" 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">L2Q5: Field Lines</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w2d1a">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w2d1a" 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_pcq_w2d1a" class="problems-wrapper" role="group"
aria-labelledby="pcq_w2d1a-problem-title"
data-problem-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w2d1a" data-url="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w2d1a/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="pcq_w2d1a-problem-title" aria-describedby="block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w2d1a-problem-progress" tabindex="-1">
Electric Field Lines
</h3>
<div class="problem-progress" id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@pcq_w2d1a-problem-progress"></div>
<div class="problem">
<div>
<p>Which of the following choices make a true statement? Check all that apply.</p>
<p>Electrostatic field lines:</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_pcq_w2d1a_2_1">
<fieldset aria-describedby="status_pcq_w2d1a_2_1">
<div class="field">
<input type="checkbox" name="input_pcq_w2d1a_2_1[]" id="input_pcq_w2d1a_2_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="pcq_w2d1a_2_1-choice_0-label" for="input_pcq_w2d1a_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_pcq_w2d1a_2_1">
<text>a) never cross.</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pcq_w2d1a_2_1[]" id="input_pcq_w2d1a_2_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="pcq_w2d1a_2_1-choice_1-label" for="input_pcq_w2d1a_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_pcq_w2d1a_2_1">
<text>b) are vectors.</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pcq_w2d1a_2_1[]" id="input_pcq_w2d1a_2_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="pcq_w2d1a_2_1-choice_2-label" for="input_pcq_w2d1a_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_pcq_w2d1a_2_1">
<text>c) start on positive charges and end on negative charges.</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pcq_w2d1a_2_1[]" id="input_pcq_w2d1a_2_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="pcq_w2d1a_2_1-choice_3-label" for="input_pcq_w2d1a_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_pcq_w2d1a_2_1">
<text>d) never form closed loops.</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_pcq_w2d1a_2_1[]" id="input_pcq_w2d1a_2_1_choice_4" class="field-input input-checkbox" value="choice_4"/><label id="pcq_w2d1a_2_1-choice_4-label" for="input_pcq_w2d1a_2_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_pcq_w2d1a_2_1">
<text>e) are lines along which electric charges move.</text>
</label>
</div>
<span id="answer_pcq_w2d1a_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_pcq_w2d1a_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<div class="solution-span">
<span id="solution_pcq_w2d1a_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Electric Field Lines" />
<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_pcq_w2d1a" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_pcq_w2d1a">
<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="pcq_w2d1a-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="pcq_w2d1a-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="pcq_w2d1a-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="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-checkpoint_w1_18" 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">L2Q6: The Sign of the Charge</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_18">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_18" 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_w1_18" class="problems-wrapper" role="group"
aria-labelledby="checkpoint_w1_18-problem-title"
data-problem-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_18" data-url="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_18/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_w1_18-problem-title" aria-describedby="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_18-problem-progress" tabindex="-1">
The sign of the charge
</h3>
<div class="problem-progress" id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_18-problem-progress"></div>
<div class="problem">
<div>
<center>
<img src="/assets/courseware/v1/b9c379a419a2140d9d3b2e1a9fdddb91/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_18_3.svg" width="330"/>
</center>
<p>
Two charged objects are fixed in space along a vertical line. The resulting electric field of the two objects is shown in the figure (only the field vectors in the plane containing the charges are shown). </p>
<p><b class="bfseries">(Part a)</b> The sign of object 1: <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_checkpoint_w1_18_2_1">
<fieldset aria-describedby="status_checkpoint_w1_18_2_1">
<div class="field">
<input type="radio" name="input_checkpoint_w1_18_2_1" id="input_checkpoint_w1_18_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="checkpoint_w1_18_2_1-choice_1-label" for="input_checkpoint_w1_18_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w1_18_2_1"> <text> positive</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_checkpoint_w1_18_2_1" id="input_checkpoint_w1_18_2_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="checkpoint_w1_18_2_1-choice_2-label" for="input_checkpoint_w1_18_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w1_18_2_1"> <text> negative</text>
</label>
</div>
<span id="answer_checkpoint_w1_18_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_checkpoint_w1_18_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><b class="bfseries">(Part b)</b> The sign of object 2: </p>
<p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div class="choicegroup capa_inputtype" id="inputtype_checkpoint_w1_18_3_1">
<fieldset aria-describedby="status_checkpoint_w1_18_3_1">
<div class="field">
<input type="radio" name="input_checkpoint_w1_18_3_1" id="input_checkpoint_w1_18_3_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="checkpoint_w1_18_3_1-choice_1-label" for="input_checkpoint_w1_18_3_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w1_18_3_1">
<text> positive</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_checkpoint_w1_18_3_1" id="input_checkpoint_w1_18_3_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="checkpoint_w1_18_3_1-choice_2-label" for="input_checkpoint_w1_18_3_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w1_18_3_1">
<text> negative</text>
</label>
</div>
<span id="answer_checkpoint_w1_18_3_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_checkpoint_w1_18_3_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_w1_18_solution_1"/>
</div></p>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="The sign of the charge" />
<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_w1_18" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_checkpoint_w1_18">
<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_w1_18-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_w1_18-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_w1_18-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="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@vertical+block@vert-checkpoint_w1_19" 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">L2Q7: Two Unknown Charges</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.1x+1T2019+type@html+block@html-checkpoint_w1_19">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-request-token="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@html+block@html-checkpoint_w1_19" 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 use the term <i>grass seeds</i> to mean a representation of field lines without the arrows shown. Under this representation, we cannot determine the sign of charges without more information, but the flow of field lines does provide some information.</p>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_20">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="ebb7a0d4ea7411efb8110e0e3c45b88f" data-usage-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_20" 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_w1_20" class="problems-wrapper" role="group"
aria-labelledby="checkpoint_w1_20-problem-title"
data-problem-id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_20" data-url="/courses/course-v1:MITx+8.02.1x+1T2019/xblock/block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_20/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_w1_20-problem-title" aria-describedby="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_20-problem-progress" tabindex="-1">
Two Unknown Charges
</h3>
<div class="problem-progress" id="block-v1:MITx+8.02.1x+1T2019+type@problem+block@checkpoint_w1_20-problem-progress"></div>
<div class="problem">
<div>
<div class="table">
<center>
<table cellspacing="0" class="tabular" style="table-layout:auto">
<tr>
<td style="text-align:center; border:none">
<img src="/assets/courseware/v1/9c78143ee769e5ae08ef88303f953afc/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_20_1.svg" width="330"/>
</td>
<td style="text-align:center; border:none">
<img src="/assets/courseware/v1/7bbfff8437e0177c255f81abc389ec6c/asset-v1:MITx+8.02.1x+1T2019+type@asset+block/images_checkpoint_w1_20_2.svg" width="330"/>
</td>
</tr>
</table>
</center>
</div>
<p>
Two objects of charge [mathjaxinline]q_1[/mathjaxinline] and [mathjaxinline]q_2[/mathjaxinline] are fixed in space along a vertical line (at the locations marked 1 and 2, respectively). The resulting grass seed representations of the electric field lines in the plane containing the objects are shown. (The direction of the field lines are not shown in grass seed images.) </p>
<p>
In the left figure, which of the following are true? (check all that apply) <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_checkpoint_w1_20_2_1">
<fieldset aria-describedby="status_checkpoint_w1_20_2_1">
<div class="field">
<input type="checkbox" name="input_checkpoint_w1_20_2_1[]" id="input_checkpoint_w1_20_2_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="checkpoint_w1_20_2_1-choice_0-label" for="input_checkpoint_w1_20_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w1_20_2_1"> <text>the charges have the same sign</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_checkpoint_w1_20_2_1[]" id="input_checkpoint_w1_20_2_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="checkpoint_w1_20_2_1-choice_1-label" for="input_checkpoint_w1_20_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w1_20_2_1"> <text>the charges have opposite sign</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_checkpoint_w1_20_2_1[]" id="input_checkpoint_w1_20_2_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="checkpoint_w1_20_2_1-choice_2-label" for="input_checkpoint_w1_20_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w1_20_2_1"> <text>[mathjaxinline]|q_1| &gt; |q_2|[/mathjaxinline]</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_checkpoint_w1_20_2_1[]" id="input_checkpoint_w1_20_2_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="checkpoint_w1_20_2_1-choice_3-label" for="input_checkpoint_w1_20_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w1_20_2_1"> <text>[mathjaxinline]|q_1| = |q_2|[/mathjaxinline]</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_checkpoint_w1_20_2_1[]" id="input_checkpoint_w1_20_2_1_choice_4" class="field-input input-checkbox" value="choice_4"/><label id="checkpoint_w1_20_2_1-choice_4-label" for="input_checkpoint_w1_20_2_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w1_20_2_1"> <text>[mathjaxinline]|q_1| &lt; |q_2|[/mathjaxinline]</text>
</label>
</div>
<span id="answer_checkpoint_w1_20_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_checkpoint_w1_20_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>
In the right figure, which of the following are true? (check all that apply) <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div class="choicegroup capa_inputtype" id="inputtype_checkpoint_w1_20_3_1">
<fieldset aria-describedby="status_checkpoint_w1_20_3_1">
<div class="field">
<input type="checkbox" name="input_checkpoint_w1_20_3_1[]" id="input_checkpoint_w1_20_3_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="checkpoint_w1_20_3_1-choice_0-label" for="input_checkpoint_w1_20_3_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w1_20_3_1"> <text>the charges have the same sign</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_checkpoint_w1_20_3_1[]" id="input_checkpoint_w1_20_3_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="checkpoint_w1_20_3_1-choice_1-label" for="input_checkpoint_w1_20_3_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w1_20_3_1"> <text>the charges have opposite sign</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_checkpoint_w1_20_3_1[]" id="input_checkpoint_w1_20_3_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="checkpoint_w1_20_3_1-choice_2-label" for="input_checkpoint_w1_20_3_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w1_20_3_1"> <text>[mathjaxinline]|q_1| &gt; |q_2|[/mathjaxinline]</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_checkpoint_w1_20_3_1[]" id="input_checkpoint_w1_20_3_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="checkpoint_w1_20_3_1-choice_3-label" for="input_checkpoint_w1_20_3_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w1_20_3_1"> <text>[mathjaxinline]|q_1| = |q_2|[/mathjaxinline]</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_checkpoint_w1_20_3_1[]" id="input_checkpoint_w1_20_3_1_choice_4" class="field-input input-checkbox" value="choice_4"/><label id="checkpoint_w1_20_3_1-choice_4-label" for="input_checkpoint_w1_20_3_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w1_20_3_1"> <text>[mathjaxinline]|q_1| &lt; |q_2|[/mathjaxinline]</text>
</label>
</div>
<span id="answer_checkpoint_w1_20_3_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_checkpoint_w1_20_3_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_w1_20_solution_1"/>
</div></p>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Two Unknown Charges" />
<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_w1_20" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_checkpoint_w1_20">
<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_w1_20-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_w1_20-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_w1_20-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>
© All Rights Reserved