115 lines
4.3 KiB
HTML
115 lines
4.3 KiB
HTML
|
<!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. 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>
|
||
|
|
|
||
|
|
<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>
|
||
|
|
</p>
|
||
|
|
<p><img src="header-index.gif" height="51" width="92"> </p>
|
||
|
|
</center>
|
||
|
|
<p><br>
|
||
|
|
</p>
|
||
|
|
</body>
|
||
|
|
</html>
|