davisnotes/mag_force_current.html

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<title>Magnetism - Force on Currents - Physics 299</title>
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<h1> <img src="ULPhys1.gif" align="texttop" height="50"
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<h1>Magnetic Forces on Electric Currents <br>
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<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>
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<font color="#ff0000"><i> </i><font color="#000000">Edward Teller</font></font><br>
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<blockquote> </blockquote>
<ul>
<li> An electric current is simply a collection of charges moving
along a wire with velocity <b>v<sub>d</sub> </b>, known as the
drift velocity.&nbsp; We have already seen that the drift
velocity and current density are related by</li>
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<div align="center"><img alt="eleccurrent eqn2"
src="elec_current_eqn2.jpg" height="54" width="126"><br>
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<div align="left">Considering the magnetic force on a single
charge (e) we find<br>
<div align="center"><img alt="magforcecurrent"
src="mag_force_current_eqn1.jpg" height="51" width="90"><br>
<br>
<div align="left">Now the total force on a wire comprised of
(nAl) charge carriers each with charge e is given by<br>
<br>
<div align="center"><img alt="magforcecurrenteqn2"
src="mag_force_current_eqn2.jpg" height="50"
width="360"><br>
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<div align="left">Defining a vector <b>l </b>along the
wire in the same direction as <b>J</b> and using |<b>J</b>A|
= i (electric current) we find for the total force on
the wire<br>
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<div align="center"><img alt="magforcecurrenteqn3"
src="mag_force_current_eqn3.jpg" height="31"
width="126"><br>
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<img alt="magforcecurrentfig1"
src="mag_force_current_fig1.jpg" height="283"
width="275">&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp;&nbsp;
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <img
alt="magforcecurrentfig2"
src="mag_force_current_fig2.jpg" height="276"
width="346"><br>
<br>
<div align="left"><img alt="exclamation"
src="exclamation-icon.gif" height="30"
width="31">&nbsp; Note that for a given current
negative and positive charge carriers move in
opposite directions.&nbsp; This leads to&nbsp; a
force on the wire in the same direction (see
above), whether the charge carriers are positive
or negative.<br>
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<font color="#ff0000"><i>When chemists die, they barium.<br>
&nbsp; </i></font><br>
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&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>
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