Module 7: Gauss's Law for Electric Fields

Folder description

Module 7 contains the following lectures and videos:

  1. Introduction to Electromagnetics Modules (7A)
  2. Instantaneous and Infinitestimal (7B)
  3. Videos of Examples (7C)
    1. Example 1.1
    2. Example 1.2
    3. Example 1.3
    4. Example 1.4
    5. Example 1.5
    6. Example 1.6
    7. Example 1.7
  4. Static Electricity Experiments (7D)
  5. Coulomb's Law (7E)
    1. Coulomb's Law - Entire Presentation
    2. Coulomb's Law - Charge Superposition
    3. Coulomb's Law - Charges and Forces
    4. Coulomb's Law - Tortional Balance

Click the Lectures & Videos link above to access the videos.

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Overview SummaryObjectives

Cell description

Summary

In this module we examine Gauss’s law and Coulomb’s law for electric charges. We find how the concepts of infinitesimal apply to electromagnetics and give some historical context. The history and results of Coulomb’s experiment and resulting equation are also presented. Many concepts that are at the heart of the physics of Electromagnetics are introduced in this module.

Objectives

By the end of this module, you will be able to:

  • Solve for the electric flux through a closed surface given the charge distribution within that surface.
  • Solve for the charge given the flux through a closed surface.
  • Given the electric field over a surface, solve for the flux through the surface and the charge enclosed by the surface.
  • Given a charge distribution construct a suitable Gaussian surface then solve for the electric field at any point in space.
  • Given the electric field over space find the divergence of the field at a point in space.
  • Describe how to find the volume of a point in space or the velocity of a moving object at an instant in time.
  • Explain the role of infinitesimal volumes in computing continuous fields and forces.
  • Identify symmetries in the three Cartesian coordinate systems.
  • Explain what a field is.
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Learning Guide

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Start by watching the Introduction to the EM modules video and reviewing the slides.  Next watch the and review the Instantaneous and Infinitesimal video and slides to review some concepts that are key to electricity and magnetism as well as calculus.  Access the podcasts for chapter 1 on the companion web site for the text book.  If you learn by listening or want to listen to the course material while commuting you can download the podcasts and listen alone or while reading the text.  You can of course listen to the podcasts when convenient on your mobile devices.  While reading the chapter work the examples and refer to the videos of each of the examples showing the solution of the examples by the instructor.  Next, view the short video presentation and slides on Coulombs law, charge superposition, charges and forces and Coulombs torsional balance.  Finally, work the homework problems at the end of chapter 1 and any other problems from chapter 1.  When you feel that you have understood the material and can work the problems you can take the quiz.The discussion questions can be found in the Discussion section below. Complete this module by submitting the module assignment. Please post any questions to the Q & A section of the Discussion Board.

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Readings

Cell description

Fleisch, D. (2008). A student's guide to Maxwell's equations. New York: Cambridge University Press.

Chapter 1 - Gauss's Law for Electirc Fields

On book web site (given below) review the coordinate systems review document as needed.  Also note the corrections for the text on this site.

The web site for the book is http://www4.wittenberg.edu/maxwell/

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Discussion Questions

Cell description

Please go to the Module 7 Discussion area and participate in the discussion forum.

Please choose and answer one or two questions from the options below.

Question 1

Discuss how gravitational force and electric force are similar and dissimilar. In electricity there are charges that both repel and attract, is this also the case for gravity?

Question 2

The electric flux is the same for a surface defined by a cube, a little sphere or a large sphere as long as the enclosed charge is the same in each case.  Yet, the electric field falls of as the inverse of the distance.  So how can the flux be the same for all the surfaces listed even though we do not specify the radius of the spheres or how large the cube is?

Question 3

What is the smallest measure of time?  Can we use this to answer a question like what is the speed of a plane in flight at noon?  Is it possible that time is not continuous but has quanta similar to electron energy states?

Question 4

On page 5 of your text it is stated the the Electric field lines are always perpendicular to the surface of a conductor in equilibrium.  Why?

Question 5

Vectors are used in Electromagnetics.  This is may not be familiar to many students.  Why do we use vectors and vector math?

Question 6

Static electricity may not seem very exciting beyond making hair stand on end or causing a spark if you walk on carpet during the winter then reach for a door knob.  But how did static electricity play a role in creating the earth and planets?

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Module 7 Assignment

Cell description

Complete the exercises at the end of chapter one and check your work and answers with the solutions shown in the textbook companion website. Post questions on the homework problems to the Module 7 Discussion forum if you do not understand the solutions. When you are comfortable with the concepts of the module, take the quiz below.

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Module 7 Quiz

Cell description

Please down load the attached quiz and complete within one hour time.  Please scan any work done by hand and attach.

The quiz has four problems.  One problem on Force due to charges, one on Electric Flux in spherical coordinates, one on charge density and one on coordinate systems. 

Total points is 137

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</li></ul></div></div>\n\n    <div class=\"vtbegenerated\"> \n <p>Please down <span><span>loa</span></span>d the attached quiz and complete within one hour time.&nbsp; Please scan any work done by hand and attach.</p> \n <p>The quiz has four problems.&nbsp; One problem on Force due to charges, one on Electric Flux in spherical coordinates, one on charge density and one on coordinate systems.&nbsp;</p> \n <p>Total points is 137</p> \n</div>\n  </div>\n\n <div id=\"_6258506_1previewModule\" class=\"moduleSample\">\n </div>\n",
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Module 7 Quiz Solutions

Cell description

The solutions for quiz 7 are linked here

Technical
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office hours recording

Cell description

see attached

Technical
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axVtbeEmbedded video\"><span data-ally-scoreindicator=\"_76869608_2\"></span></span>\n<a href=\"/bbcswebdav/pid-6258508-dt-content-rid-76869608_2/xid-76869608_2\" target=\"_blank\"><img src=\"/images/ci/ng/cal_year_event.gif\" alt=\"File\">&nbsp;zoom_0.mp4</a> \n<span class=\"contextMenuContainer video\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.525.201.81.SP19/Mod07/zoom_0.mp4?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00rk&amp;course_id=_177474_1&amp;ctxMenuXythosId=76869608_2&amp;course_id=_177474_1\" bb:navitem=\"\" bb:contextparameters=\"\" 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src=\"/webapps/cmsmain/dirlistrightframe/dirlist.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/static/bbDriveUtil.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\">\n    (function(){\n     var f = function(){\n           if ( window.DWREngine )\n      {\n       if( DWREngine._batch )\n       {\n      \t try {DWREngine.endBatch();} catch(ignore) {}\n       }\n       try {DWREngine.beginBatch();} catch(ignore) {}\n      } \n             page.ContextMenu.hideMenuDiv('240692759dd64a46a3e35bb590e2449b');\n            if ( window.DWREngine )\n      {\n        try {DWREngine.endBatch();} catch(ignore) {}\n      }\n               };\n     var f2 = function()\n     {\n       if ( page.isLoaded )\n       {\n         f();\n       }\n       else\n       {\n         setTimeout( f2, 500 );\n       }\n     }\n     f2();\n    })();\n   </script> (<span id=\"/xid-76869608_2_fileSize\">17.138 MB</span>) </li></ul></div></div>\n\n    <div class=\"vtbegenerated\"> \n <p>see attached</p> \n</div>\n  </div>\n\n <div id=\"_6258508_1previewModule\" class=\"moduleSample\">\n </div>\n",
        "url": "https://blackboard.jhu.edu/webapps/blackboard/content/listContent.jsp?course_id=_177474_1&content_id=_6258499_1#",
        "title": "\n    \n  \n\n\n\n     office hours recording\n \n"
    },
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axVtbeEmbedded video\"><span data-ally-scoreindicator=\"_76869608_2\"></span></span>\n<a href=\"/bbcswebdav/pid-6258508-dt-content-rid-76869608_2/xid-76869608_2\" target=\"_blank\"><img src=\"/images/ci/ng/cal_year_event.gif\" alt=\"File\">&nbsp;zoom_0.mp4</a> \n<span class=\"contextMenuContainer video\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.525.201.81.SP19/Mod07/zoom_0.mp4?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00rk&amp;course_id=_177474_1&amp;ctxMenuXythosId=76869608_2&amp;course_id=_177474_1\" bb:navitem=\"\" bb:contextparameters=\"\" 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src=\"/webapps/cmsmain/dirlistrightframe/dirlist.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/static/bbDriveUtil.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\">\n    (function(){\n     var f = function(){\n           if ( window.DWREngine )\n      {\n       if( DWREngine._batch )\n       {\n      \t try {DWREngine.endBatch();} catch(ignore) {}\n       }\n       try {DWREngine.beginBatch();} catch(ignore) {}\n      } \n             page.ContextMenu.hideMenuDiv('240692759dd64a46a3e35bb590e2449b');\n            if ( window.DWREngine )\n      {\n        try {DWREngine.endBatch();} catch(ignore) {}\n      }\n               };\n     var f2 = function()\n     {\n       if ( page.isLoaded )\n       {\n         f();\n       }\n       else\n       {\n         setTimeout( f2, 500 );\n       }\n     }\n     f2();\n    })();\n   </script> (<span id=\"/xid-76869608_2_fileSize\">17.138 MB</span>) </li></ul></div></div>\n\n    <div class=\"vtbegenerated\"> \n <p>see attached</p> \n</div>\n  </div>\n\n <div id=\"_6258508_1previewModule\" class=\"moduleSample\">\n </div>\n",
    "url": "https://blackboard.jhu.edu/webapps/blackboard/content/listContent.jsp?course_id=_177474_1&content_id=_6258499_1#",
    "parent": 115,
    "has_attachments": 0,
    "rendered": {
        "title": "office hours recording",
        "body": "\n      \n\n    <div> \n <p>see attached</p> \n</div>\n  "
    },
    "attachments": [
        {
            "id": 562,
            "name": "file_0.mp4",
            "location": "./attachments/cell_520/file_0.mp4",
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                "title": "file_0.mp4",
                "url": "https://blackboard.jhu.edu/bbcswebdav/pid-6258508-dt-content-rid-76869608_2/xid-76869608_2",
                "mime": "video/mp4",
                "file": "./attachments/cell_520/file_0.mp4",
                "icon": "file-video"
            },
            "parent": 520,
            "ordering": 0,
            "link": "./player.html?parent=115&video=./attachments/cell_520/file_0.mp4&name=file_0.mp4&parent_name=office%20hours%20recording"
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}