155 lines
5.6 KiB
HTML
155 lines
5.6 KiB
HTML
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<!DOCTYPE HTML PUBLIC "-//w3c//dtd html 4.0 transitional//en">
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<html>
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<head>
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<meta http-equiv="Content-Type"
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content="text/html; charset=ISO-8859-1">
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<meta name="GENERATOR"
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content="Mozilla/4.7 [en] (X11; U; OSF1 V4.0 alpha) [Netscape]">
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<meta name="Author" content="C. L. Davis">
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<title>Electricity - Coulomb's Law - Physics 299</title>
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</head>
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<body style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);"
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alink="#ff0000" link="#0000ee" vlink="#551a8b">
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<center>
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<h1> <img src="ULPhys1.gif" align="texttop" height="50" width="189"></h1>
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</center>
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<center>
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<h1>Coulomb's Law</h1>
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</center>
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<center><img src="celticbar.gif" height="22" width="576"><br>
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<br>
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<font color="#ff0000"><i>"When man wanted to make a machine that would
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walk
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he created the wheel, which does not resemble a leg"</i></font><br>
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Guillaume Apollinaire<br>
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</center>
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<img src="netbar.gif" align="middle" height="40" width="100%"> <br>
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<ul>
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<li> The magnitude of the force of attraction (or repulsion), F<sub>12</sub>
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between two point charges q<sub>1</sub> and q<sub> 2 </sub> is
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given by Coulomb's Law.</li>
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<center>
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<p><br>
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<img alt="" src="elec_coulomb_eqn1.gif"
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style="width: 80px; height: 47px;"> <br>
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</p>
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</center>
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<p>where R<sub>12</sub> is the distance between the
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charges. k is a constant of proportionality known as the Coulomb
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constant, having the value 9 x
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10<sup>9</sup> N.m<sup>2</sup> / C<sup>2</sup> in a
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vacuum. </p>
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<p><img style="width: 31px; height: 30px;" alt="exclamation"
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src="exclamation-icon.gif"> Note that the Coulomb constant, k, is
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often replaced with (1/4π ε<sub>0</sub>), where
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ε<sub>0</sub>is the permittivity of the vacuum (more later).<br>
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</p>
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<li> The direction of this force is along the line joining the two
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charges
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with the sense determined by the relative signs of the charges</li>
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<p><br>
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</p>
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<center>
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<p><img src="coulaw1.gif" height="112" width="182"> </p>
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</center>
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<li> Note that the force on each charge has the same magnitude (as
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required by Newton's third law of motion).</li>
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<br>
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<li> For two 1 Coulomb charges separated by 1 metre the
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magnitude
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of the force is given by,
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<center> <br>
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F = (9 x 10<sup>9</sup> x 1 x 1 )/ 1 = 9 x 10<sup>9</sup>
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Newtons</center>
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<p>This is an <b><i>extremely large</i></b> force (sufficient to
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move Mt. Everest with an acceleration of 1cm/s<sup>2</sup>). The
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Coulomb
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is a <b><i>very large</i></b> unit. Typical macroscopic charges
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are measured in micro-coulombs (10<sup>-6</sup> C). </p>
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</li>
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<li>To handle situations with more than one charge, the charges must
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be treated in pairs, so that the overall force on one charge will be
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the <span style="font-weight: bold;">vector</span> sum of the force
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due to each of the other charges. For example the force on q<sub>1</sub>
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due to all other charges q<sub>2</sub>, q<sub>3</sub> , q<sub>4</sub>...
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would
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be
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given
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by,</li>
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</ul>
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<div style="text-align: center;"><span style="font-weight: bold;">F</span><sub
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style="font-weight: bold;">1</sub><span style="font-weight: bold;"> = F</span><sub
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style="font-weight: bold;">21</sub><span style="font-weight: bold;"> +
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F</span><sub style="font-weight: bold;">31</sub><span
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style="font-weight: bold;"> + F</span><sub style="font-weight: bold;">41</sub><span
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style="font-weight: bold;"> + ...</span><br>
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<div style="text-align: left;">
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<ul>
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<li><img style="width: 79px; height: 43px;" alt="hot" src="hot.gif">Notice
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the
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similarity
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of
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Coulomb's Law to Newton's Law of Gravitation</li>
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</ul>
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<div style="text-align: center;"><img
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style="border: 0px solid ; width: 114px; height: 62px;" alt="eqn1"
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src="grav_eqn1.jpg"><br>
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<div style="text-align: left; margin-left: 40px;"><br>
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both are "inverse square" laws. Substitute charge for mass and
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"k" for "G" and you have Coulomb's law.<br>
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<img style="width: 31px; height: 30px;" alt="exclamation"
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src="exclamation-icon.gif"> The relative magnitudes of the Coulomb
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constant, k = 9 x 10<sup>9</sup> and the gravitational constant, G =
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6.67 x 10<sup>-11</sup>, is an indication of the relative strengths of
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the two forces. The electrical force of attraction is much, much
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stronger than the gravitational force of attraction.<br>
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</div>
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</div>
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</div>
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</div>
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<ul>
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</ul>
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<p><br>
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<img src="netbar.gif" height="40" width="100%"> </p>
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<center><span
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style="font-size: 12pt; font-family: "Times New Roman"; color: rgb(255, 0, 0); font-style: italic;">"The
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wireless
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telegraph
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is
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not
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difficult
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to
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understand. The ordinary telegraph is like a very long cat. You pull
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the tail
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in </span><st1:state style="color: rgb(255, 0, 0); font-style: italic;"><st1:place><span
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style="font-size: 12pt; font-family: "Times New Roman";">New York</span></st1:place></st1:state><span
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style="font-size: 12pt; font-family: "Times New Roman"; color: rgb(255, 0, 0); font-style: italic;">,
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and
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it
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meows
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in
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</span><st1:city style="color: rgb(255, 0, 0); font-style: italic;"><st1:place><span
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style="font-size: 12pt; font-family: "Times New Roman";">Los Angeles</span></st1:place></st1:city><span
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style="font-size: 12pt; font-family: "Times New Roman";"><span
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style="color: rgb(255, 0, 0); font-style: italic;">. The wireless is
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the same, only without the cat."</span><br>
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Albert Einstein<br>
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</span><br>
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<img src="celticbar.gif" height="22" width="576"> <br>
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<p><i>Dr. C. L. Davis</i> <br>
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<i>Physics Department</i> <br>
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<i>University of Louisville</i> <br>
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<i>email</i>: <a href="mailto:c.l.davis@louisville.edu">c.l.davis@louisville.edu</a>
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<br>
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</p>
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<p><img src="header-index.gif" height="51" width="92">
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</p>
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</center>
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<p><br>
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</p>
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</body>
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</html>
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