240 lines
11 KiB
HTML
240 lines
11 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" content="text/html;
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charset=windows-1252">
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<meta name="GENERATOR" content="Mozilla/4.7 [en] (X11; U; OSF1 V4.0
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alpha) [Netscape]">
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<meta name="Author" content="C. L. Davis">
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<title>Magnetism - Motion of Charged Particles in B and E - Physics
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299</title>
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<meta content="C. L. Davis" name="author">
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</head>
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<body style="color: rgb(0, 0, 0); background-color: rgb(255, 255,
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255);" link="#0000ee" alink="#ff0000" vlink="#551a8b">
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<center>
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<h1> <img src="ULPhys1.gif" height="50" align="texttop"
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width="189"></h1>
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</center>
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<center>
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<h1>Motion of Charged Particles in Magnetic and Electric Fields<br>
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</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>
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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</i></font><font color="#ff0000"><i>
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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</i></font>
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<div class="copy-paste-block"><font color="#ff0000"><i><span
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class="bqQuoteLink">"A</span></i></font><font
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color="#ff0000"><i><span class="bqQuoteLink"> fact is a simple
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statement that everyone believes. It is innocent,
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unless found guilty. A hypothesis is a novel
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suggestion that no one wants to believe. It is
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guilty, until found effective</span></i><span></span>"</font><br>
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</div>
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<font color="#ff0000"><i> </i><font color="#000000">Edward Teller</font></font><br>
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</center>
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<img src="netbar.gif" height="40" align="middle" width="100%">
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<blockquote> </blockquote>
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<div align="center">
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<div align="left">
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<div align="center">
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<div align="left">
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<div align="center">
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<div align="left">
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<div align="center">
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<div align="left">
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<div align="center">
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<div align="left">
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<div align="center"><font color="#6600cc"><big><u><b>MAGNETIC
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FIELDS</b></u></big></font></div>
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<ul>
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<li>Return now to the case of a "point" charge
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moving with velocity <b>v</b> in a region
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of constant magnetic field (<b>B</b>).
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We previously stated (without proof) that
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such a particle would move in a circle or
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helix. Now let's prove it.</li>
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</ul>
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<ul>
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<li> <img alt="magforcechargefig2"
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src="mag_force_charge_fig2.jpg"
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height="324" align="right" width="292">Consider
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the positive charge (e) at the top of the
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figure at right. With the directions
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of <b>v</b> and <b>B</b> indicated the
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right-hand-rule leads to a downwards force
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as shown. This force changes the
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direction of <b>v</b> but does not change
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the magnitude of <b>v</b>, as shown.</li>
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</ul>
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<ul>
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<li>Quantitatively we find</li>
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</ul>
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<div align="center"><img alt="magmotionch"
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src="mag_motionch_eqn1.jpg" height="37"
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width="180"><br>
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<blockquote>
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<div align="left">Assuming that this force
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causes circular motion, <b>F<sub>B</sub>
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</b>is the centripetal force so that<br>
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<br>
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<div align="center"><img
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alt="magmotioneqn2"
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src="mag_motionch_eqn2.jpg"
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height="64" width="108"><br>
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<div align="left">which leads to a
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radius<br>
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</div>
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</div>
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</div>
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</blockquote>
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</div>
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<div align="center"><img alt="magmotioncheqn3"
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src="mag_motionch_eqn3.jpg" height="63"
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width="72"><br>
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<blockquote>
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<div align="left">The period (time taken to
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perform one revolution) is given by<br>
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<br>
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<div align="center"><img
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alt="magmotioncheqn4"
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src="mag_motionch_eqn4.jpg"
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height="56" width="225"><br>
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<div align="left">The frequency, f, is<br>
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<div align="center"><img
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alt="magmotioncheqn5"
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src="mag_motionch_eqn5.jpg"
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height="62" width="135"><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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</blockquote>
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<div align="left">
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<ul>
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<li><img alt="exclamation"
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src="exclamation-icon.gif" height="30"
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width="31"> Notice that this frequency
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is independent of the velocity.
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That is fast particles will move in
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large radius circles, slow
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particles will have smaller radii.
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This phenomenon is the basis for the
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cyclotron one of the earliest charged
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particle accelerators.</li>
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</ul>
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<ul>
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<li><img alt="exclamation"
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src="exclamation-icon.gif" height="30"
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width="31"> If the velocity of
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the particle has a component along <b>B</b>
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this will be unchanged and the resultant
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trajectory will be helical.</li>
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</ul>
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<div align="center"><img alt="divider"
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src="divider_ornbarblu.gif" height="64"
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width="393"><br>
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<br>
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<font color="#6600cc"><big><u><b>MAGNETIC
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and ELECTRIC FIELDS</b></u></big></font><br>
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</div>
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<ul>
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<li>There are many useful applications in
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which <b>B</b> and <b>E</b> fields are
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applied simultaneously. Perhaps
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the simplest application is the
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"crossed" <b>B</b> and <b>E</b>
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fields. </li>
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</ul>
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<div align="center"><img
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alt="magmotionchfig1"
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src="mag_motionch_fig1.gif" height="174"
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width="311"></div>
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<ul>
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</ul>
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<blockquote>
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<p>For this configuration the electric and
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magnetic forces are in opposite
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directions. If a charged particle
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moves through this region of space with
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no deflection then</p>
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<p align="center"><img
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alt="magmotioncheqn6"
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src="mag_motionch_eqn6.jpg"
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height="32" width="189"><br>
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</p>
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<div align="left">so that<br>
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<div align="center">
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<div align="center"><img
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alt="magmotioncheqn7"
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src="mag_motionch_eqn7.jpg"
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height="54" width="54"><br>
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<div align="left"><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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</blockquote>
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<div align="left">
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<div align="center">
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<div align="center">
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<div align="left">
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<ul>
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<li>Other applications include
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mass spectrometers and particle
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accelerators. (<b>EXPAND
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?)</b><br>
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</li>
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</ul>
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</div>
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</div>
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</div>
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</div>
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<img src="netbar.gif" height="40"
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width="100%"> </div>
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</div>
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</div>
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</div>
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</div>
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</div>
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</div>
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</div>
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</div>
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</div>
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</div>
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</div>
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<center>
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<p style="color: rgb(255, 0, 0); font-style: italic;"
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class="MsoNormal">
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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</p>
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<font color="#ff0000"><i>I'm reading a book about
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anti-gravity. I can't put it down. </i></font><br>
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<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"> </p>
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</center>
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<p><br>
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</p>
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<blockquote> </blockquote>
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</body>
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</html>
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