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<!DOCTYPE html PUBLIC "-//w3c//dtd html 4.0 transitional//en">
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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>Magnetism - Force Between Parallel Wires: Ampere Definition -
Physics 299</title>
<meta content="C. L. Davis" name="author">
</head>
<body style="color: rgb(0, 0, 0); background-color: rgb(255, 255,
255);" link="#0000ee" vlink="#551a8b" alink="#ff0000">
<center>
<h1> <img src="ULPhys1.gif" height="50" width="189"
align="texttop"></h1>
</center>
<center>
<h1>Force Between Two Parallel Wires: Ampere Definition <br>
</h1>
</center>
<center><img src="celticbar.gif" height="22" width="576"><br>
<br>
<font color="#ff0000"><i>
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charset=windows-1252">
</i></font><font color="#ff0000"><i>
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charset=windows-1252">
</i></font>
<div class="copy-paste-block"><font color="#ff0000"><i><span
class="bqQuoteLink">"A</span></i></font><font
color="#ff0000"><i><span class="bqQuoteLink"> fact is a simple
statement that everyone believes.&nbsp; It is innocent,
unless found guilty.&nbsp; A hypothesis is a novel
suggestion that no one wants to believe.&nbsp; It is
guilty, until found effective</span></i><span></span>"</font><br>
</div>
<font color="#ff0000"><i> </i><font color="#000000">Edward Teller</font></font><br>
</center>
<img src="netbar.gif" height="40" width="100%" align="middle">
<blockquote> </blockquote>
<ul>
<li> We have just seen that a long straight wire carrying current
i<sub>1</sub>&nbsp; produces a <b>B</b> field which forms
concentric circles around the wire whose magnitude a distance
"d" from the wire is given by <br>
</li>
</ul>
<div align="center"><img alt="magforce2wireseqn1"
src="mag_force_2wires_eqn1.jpg" height="73" width="108"><br>
<blockquote>
<div align="left">with direction given by "the" right-hand-rule.<br>
</div>
</blockquote>
<div align="left">
<ul>
<li><img alt="magforce2wiresfig1"
src="mag_force_2wires_fig1.jpg" height="340" width="245"
align="right">If a second parallel wire carrying a current
i<sub>2</sub> is placed a distance "d" from the first, it
will feel a force due to the presense of <b>B<sub>1</sub> </b>.&nbsp;
The force felt by a length l<sub>2</sub>&nbsp; of this
second wire is</li>
</ul>
<div align="center"><img alt="magforce2wireseqn2"
src="mag_force_2wires_eqn2.jpg" height="32" width="149"><br>
<blockquote>
<div align="left">so that<br>
<div align="center"><img alt="magforce2wireseqn3"
src="mag_force_2wires_eqn3.jpg" height="69"
width="144"><br>
<br>
<div align="left">with a direction such that i<sub>2</sub>
is attracted towards i<sub>1</sub> as shown at right.<br>
Then the force per unit length on i<sub>2</sub> is
given by<br>
<div align="center"><img alt="magforce2wireseqn4"
src="mag_force_2wires_eqn4.jpg" height="76"
width="119"><br>
</div>
</div>
</div>
</div>
</blockquote>
<div align="left">
<div align="center">
<div align="left">
<ul>
<li><img alt="exclamation" src="exclamation-icon.gif"
height="30" width="31"> Note that if we reverse
the roles of i<sub>1</sub> and i<sub>2</sub> we
obtain the same expression for F<sub>1</sub>/l<sub>1</sub>
.&nbsp; That is, i<sub>1</sub> exerts a force
on&nbsp; i<sub>2</sub> and&nbsp; i<sub>2</sub>&nbsp;
exerts an equal, but opposite, force on i<sub>1</sub>&nbsp;
as expected from Newton's Third Law ("Action equals
Reaction").</li>
</ul>
<ul>
<li>The above analysis applies for parallel currents -
the two wires are attracted to each other.&nbsp; If
one of the currents is reversed, so that the
currents are "anti-parallel", the force per unit
length is unchanged, but the force acting on each
wire is reversed.&nbsp; In other words the wires are
now repelled from each other.</li>
</ul>
<blockquote><img alt="exclamation"
src="exclamation-icon.gif" height="30" width="31"> <i><b>"Like
currents are attractive, unlike currents are
repelled"</b></i>.&nbsp; Note that this is
opposite to the behavior of point electric charges.<br>
<br>
</blockquote>
<ul>
<li><big><big><font color="#cc33cc"><u><i><b>Definition
of the Ampere</b></i></u></font></big></big></li>
</ul>
<blockquote>
<p>The unit of electric current, the Ampere, is
defined using the force between parallel wires
carrying current.<br>
</p>
<p align="center"><img alt="tick" src="tickred1.gif"
height="48" width="48"><big><i><b>"The Ampere is
that current which when flowing in two
infinite parallel wires</b></i><i><b> one
metre apart produces a force between them of 2
x 10</b></i><i><b><sup>-7</sup></b></i><i><b>
N/m"</b></i><i><b> </b></i></big><br>
<br>
</p>
<p align="left">Proof:<br>
</p>
<div align="center"><img alt="magforce2wireseqn5"
src="mag_force_2wires_eqn5.jpg" height="71"
width="479"></div>
</blockquote>
</div>
</div>
</div>
</div>
</div>
</div>
<img src="netbar.gif" height="40" width="100%">
<div align="center">
<div align="center"> </div>
<center>
<p style="color: rgb(255, 0, 0); font-style: italic;"
class="MsoNormal">
<meta http-equiv="content-type" content="text/html;
charset=windows-1252">
</p>
<font color="#ff0000"><i>What do you call a dinosaur with an
extensive vocabulary ?&nbsp; A thesaurus. </i></font><br>
<br>
&nbsp;<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>
<blockquote> </blockquote>
</div>
</body>
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