davisnotes/elec_contdist.html

97 lines
3.8 KiB
HTML
Raw Normal View History

2016-05-20 00:56:25 -04:00
<!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 Field Due to Continuous Charge
Distributions - Physics 299</title>
</head>
<body style="color: rgb(0, 0, 0); background-color: rgb(255, 255,
255);" link="#0000ee" alink="#ff0000" bgcolor="#ff0000"
text="#000000" vlink="#551a8b">
<center>
<h1> <img src="ULPhys1.gif" height="50" align="texttop"
width="189"></h1>
</center>
<center>
<h1>Electric Field Due Continuous Charge Distribtuions<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">
Common sense is the collection of prejudices acquired by age
eighteen"</i></font><br>
Albert Einstein<br>
</center>
<img src="netbar.gif" height="40" align="middle" width="100%"> <br>
<ul>
</ul>
<ul>
<li>Electric charge is a property of individual particles -
protons, electrons etc.&nbsp; But since these particles are
extremely small it is often convenient to consider charge to be
continuously distributed.&nbsp; <br>
</li>
</ul>
<ul>
<li>These distributions can be over a line (one dimension), an
area (two dimensions) or a volume (three dimensions).</li>
</ul>
<ul>
<li>In order to determine the electric field due to a continuous
charge distribution we "sum" the fields due to the individual
"elements" that comprise the distribution, by integrating over
the line, area or volume in question.&nbsp; For example in the
example below charge is distributed uniformly over the rod on
the x axis.&nbsp; To determine the electric field at point P, we
write down the expression for the field at P due to the "point"
charge dq located at "x" as shown, then integrate over x from x
= 0 to x = x. <br>
</li>
</ul>
<div align="center"><img alt="contin charge dist"
src="elec_continchgdist.jpg" height="244" width="272"><br>
</div>
<ul>
</ul>
<br>
<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: &quot;Times New
Roman&quot;;"><span style="color: rgb(255, 0, 0); font-style:
italic;"></span></span><span style="font-size: 12pt;
font-family: &quot;Times New Roman&quot;;"><span style="color:
rgb(255, 0, 0); font-style: italic;">
<meta http-equiv="content-type" content="text/html;
charset=windows-1252">
</span></span><br>
<i><font color="#ff0000">Overheard after a student failed a
physics test miserably:
Nuclear, Hydrogen, Atomic, My test- They can all be bombs.</font></i><br>
<span style="font-size: 12pt; font-family: &quot;Times New
Roman&quot;;"><span style="color: rgb(255, 0, 0); font-style:
italic;"></span></span> <br>
<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>