118 lines
4.6 KiB
HTML
118 lines
4.6 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>Electricity - Electric Dipole in an External Field - Physics
|
|
299</title>
|
|
</head>
|
|
<body style="color: rgb(0, 0, 0); background-color: rgb(255, 255,
|
|
255);" link="#0000ee" alink="#ff0000" vlink="#551a8b">
|
|
<center>
|
|
<h1> <img src="ULPhys1.gif" height="50" align="texttop"
|
|
width="189"></h1>
|
|
</center>
|
|
<center>
|
|
<h1>Electric Dipole in an External Electric Field <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">
|
|
When you look at yourself from a universal standpoint,
|
|
something inside always reminds or informs you that there are
|
|
bigger and better things to worry about."</i></font><br>
|
|
Albert Einstein<br>
|
|
</center>
|
|
<img src="netbar.gif" height="40" align="middle" width="100%"> <br>
|
|
<ul>
|
|
</ul>
|
|
<ul>
|
|
<li>We have already considered the electric field <i><b>created</b></i>
|
|
by an electric dipole. Now we consider the behavior of an
|
|
electric dipole placed in a uniform (constant) electric field.</li>
|
|
</ul>
|
|
<div align="center"><img alt="elec dip in external field"
|
|
src="elec_dip_exte.gif" height="157" width="323"><br>
|
|
<br>
|
|
<div align="left">
|
|
<ul>
|
|
<li>Note that since the force on each of the charges are equal
|
|
in magnitude but opposite in direction there is <b>no net
|
|
force on the dipole</b>.</li>
|
|
</ul>
|
|
<ul>
|
|
<li>However, since the two forces are not concurrent, there is
|
|
a non-zero torque about the center of the dipole given by,</li>
|
|
</ul>
|
|
<div align="center"><img alt="elec dip ext e eqn1"
|
|
src="elec_dipexte_eqn1.jpg" height="45" width="117"><br>
|
|
<br>
|
|
<div align="left">
|
|
<ul>
|
|
<li>Using the definition of the work done by a torque
|
|
(rotational force), it can be shown that the
|
|
electrical potential energy stored by a dipole in an
|
|
external field is given by,</li>
|
|
</ul>
|
|
<div align="center"><img alt="elec dip in ext e eqn2"
|
|
src="elec_dipexte_eqn2.jpg" height="41" width="117"><br>
|
|
<div align="left">
|
|
<ul>
|
|
<li><img alt="hot" src="hot.gif" height="43"
|
|
align="middle" width="79">A dipole placed in a
|
|
uniform electric field will rotate until it is
|
|
aligned "-" to "+" along the field - this is the
|
|
lowest energy configuration.</li>
|
|
</ul>
|
|
<ul>
|
|
<li><img alt="exclamation" src="exclamation-icon.gif"
|
|
height="30" width="31"> If the external
|
|
field is not uniform, the net force will not be
|
|
zero.<br>
|
|
</li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<ul>
|
|
</ul>
|
|
<ul>
|
|
</ul>
|
|
<div align="center"> </div>
|
|
<div style="text-align: left;"><img src="netbar.gif" height="40"
|
|
width="100%"> </div>
|
|
<center><span style="font-size: 12pt; font-family: "Times New
|
|
Roman";"><span style="color: rgb(255, 0, 0); font-style:
|
|
italic;"></span></span><span style="font-size: 12pt;
|
|
font-family: "Times New Roman";"><span style="color:
|
|
rgb(255, 0, 0); font-style: italic;">
|
|
<meta http-equiv="content-type" content="text/html;
|
|
charset=windows-1252">
|
|
</span></span><br>
|
|
<font color="#ff0000"><i>What is a quantum particle?
|
|
The dreams that stuff is made of!</i></font><br>
|
|
<br>
|
|
<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>
|