115 lines
4.3 KiB
HTML
115 lines
4.3 KiB
HTML
<!DOCTYPE html PUBLIC "-//w3c//dtd html 4.0 transitional//en">
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<html>
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<head>
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<meta http-equiv="Content-Type" content="text/html;
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charset=windows-1252">
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<meta name="GENERATOR" content="Mozilla/4.7 [en] (X11; U; OSF1 V4.0
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alpha) [Netscape]">
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<meta name="Author" content="C. L. Davis">
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<title>Electricty - Electric Field from Electric Potential - Physics
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299</title>
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</head>
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<body style="color: rgb(0, 0, 0); background-color: rgb(255, 255,
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255);" alink="#ff0000" link="#0000ee" vlink="#551a8b">
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<center><img src="ULPhys1.gif" align="texttop" height="50"
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width="189"></center>
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<center>
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<h1>Determining the Electric Field from the Electric Potential<br>
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</h1>
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</center>
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<center><img src="celticbar.gif" height="22" width="576"><br>
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<br>
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<font color="#ff0000"><i>"</i></font><font color="#ff0000"><i>
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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</i></font><font color="#ff0000"><i>
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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I've found out so much about electricity that I've reached the
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point where I understand nothing and can explain nothing"<br>
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<i>[Describing his experiments with the Leyden jar.]</i></i></font><br>
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Pieter van Musschenbroek<br>
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</center>
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<img src="netbar.gif" align="middle" height="40" width="100%"> <br>
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<br>
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<ul>
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<li>Suppose we are given the electric potential, V, as a function
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of position. Is it possible to determine the <b>E</b>
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field from this V ?</li>
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</ul>
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<blockquote>Starting from the definition of the potential difference
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in terms of the <b>E</b> field,<br>
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<div align="center"><img alt="elec pot eqn2"
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src="elec_potential_eqn2.jpg" height="75" width="519"><br>
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<br>
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<div align="left">then if the path A to B is along the x axis we
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obtain,<br>
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<div align="center"><img alt="elec pot efromV eqn1"
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src="elec_potential_efromV_eqn1.png" height="43"
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width="152"><br>
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</div>
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</div>
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</div>
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</blockquote>
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<div align="center">
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<div align="left">
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<div align="center">
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<div align="left">
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<ul>
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<li>This expression can be written in the alternative
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form,</li>
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</ul>
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<div align="center"><img alt="eqn2"
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src="elec_potential_efromV_eqn2a.jpg" height="55"
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width="92"><br>
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<br>
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<blockquote>
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<div align="left">If the path A to B is in an arbitrary
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direction we obtain the most general expression of "E
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from V",<br>
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<br>
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<div align="center"><img alt="elec pot efromV eqn3"
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src="elec_potential_efromV_eqn3.png" height="66"
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width="507"><br>
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</div>
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</div>
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</blockquote>
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</div>
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</div>
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</div>
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</div>
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</div>
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<blockquote>
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<div align="center">
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<div align="left"> </div>
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</div>
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</blockquote>
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<img src="netbar.gif" height="40" width="100%">
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<center>
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<p class="MsoNormal"><span style="color: rgb(255, 0, 0);
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font-style: italic;">
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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"</span><span style="color: rgb(255, 0, 0); font-style:
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italic;">
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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I am an expert of electricity. My father occupied the chair of
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applied electricity at the state prison."</span><br>
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W. C. Fields<br>
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</p>
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<img src="celticbar.gif" height="22" width="576"> <br>
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<p><i>Dr. C. L. Davis</i> <br>
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<i>Physics Department</i> <br>
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<i>University of Louisville</i> <br>
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<i>email</i>: <a href="mailto:c.l.davis@louisville.edu">c.l.davis@louisville.edu</a>
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<br>
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</p>
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<p><img src="header-index.gif" height="51" width="92"> </p>
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</center>
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<p><br>
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</p>
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</body>
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</html>
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