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