https://physwiki.com/w/index.php?action=history&feed=atom&title=EM_Course_Notes 2026-06-17T00:30:53Z Revision history for this page on the wiki MediaWiki 1.20.4 https://physwiki.com/w/index.php?title=EM_Course_Notes&diff=10958&oldid=prev 2015-01-25T03:53:27Z

<p>‎<span dir="auto"><span class="autocomment">Exercises</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black;">← Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 03:53, 25 January 2015</td> </tr><tr><td colspan="2" class="diff-lineno">Line 51:</td> <td colspan="2" class="diff-lineno">Line 51:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>&#160; &lt;/div&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>&#160; &lt;/div&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>===''&lt;small&gt;Exercises&lt;/small&gt;''===</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>===''&lt;small&gt;Exercises&lt;/small&gt;''===</div></td></tr> <tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>[http://physwiki.com/w/images/a/a3/210A_Comp_Q1_%26_Sol.pdf&#160; Disc 1 <del class="diffchange diffchange-inline">Q&amp;A</del>]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>[http://physwiki.com/w/images/a/a3/210A_Comp_Q1_%26_Sol.pdf&#160; Disc 1<ins class="diffchange diffchange-inline">]</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">[http://physwiki.com/w/images/e/e8/F11Q10.pdf Disc 2</ins>]</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>==210B Notes==</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>==210B Notes==</div></td></tr> </table>

Tom Neiser https://physwiki.com/w/index.php?title=EM_Course_Notes&diff=10956&oldid=prev 2015-01-14T17:52:36Z

<p>‎<span dir="auto"><span class="autocomment">221A Notes</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black;">← Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 17:52, 14 January 2015</td> </tr><tr><td colspan="2" class="diff-lineno">Line 4:</td> <td colspan="2" class="diff-lineno">Line 4:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>==<del class="diffchange diffchange-inline">221A </del>Notes==</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>==<ins class="diffchange diffchange-inline">210A </ins>Notes==</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>'''Electrostatics'''</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>'''Electrostatics'''</div></td></tr> </table>

Tom Neiser https://physwiki.com/w/index.php?title=EM_Course_Notes&diff=10955&oldid=prev 2015-01-14T17:51:28Z

<p>‎<span dir="auto"><span class="autocomment">Exercises</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black;">← Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 17:51, 14 January 2015</td> </tr><tr><td colspan="2" class="diff-lineno">Line 51:</td> <td colspan="2" class="diff-lineno">Line 51:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>&#160; &lt;/div&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>&#160; &lt;/div&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>===''&lt;small&gt;Exercises&lt;/small&gt;''===</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>===''&lt;small&gt;Exercises&lt;/small&gt;''===</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">[http://physwiki.com/w/images/a/a3/210A_Comp_Q1_%26_Sol.pdf&#160; Disc 1 Q&amp;A]</ins></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>==210B Notes==</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>==210B Notes==</div></td></tr> </table>

Tom Neiser https://physwiki.com/w/index.php?title=EM_Course_Notes&diff=10608&oldid=prev 2014-05-13T02:17:59Z

<p>‎<span dir="auto"><span class="autocomment">210B Notes</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black;">← Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 02:17, 13 May 2014</td> </tr><tr><td colspan="2" class="diff-lineno">Line 180:</td> <td colspan="2" class="diff-lineno">Line 180:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>&lt;/div&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>&lt;/div&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">===''&lt;small&gt;Exercises&lt;/small&gt;''===</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">'''Q1:''' A pulsar emits bursts of radio waves at two frequencies $\omega_1$, $\omega_2$. The pulses arrive at different times $t_1$, $t_2$ due to interaction with the interstellar medium- a dilute Hydrogen plasma. Find the distance $s$ from pulsar to earth, given $\tau= t_2 - t_2$. (F'12Q12)&lt;div class=&quot;mw-collapsible mw-collapsed&quot; style=&quot;width:750px&quot;&gt;</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">See [[Fall_2012#Question_12| F'12Q12]]. </del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">&lt;/div&gt;</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">===''&lt;small&gt;Exercises&lt;/small&gt;''===</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">'''Q1:''' A pulsar emits bursts of radio waves at two frequencies $\omega_1$, $\omega_2$. The pulses arrive at different times $t_1$, $t_2$ due to interaction with the interstellar medium- a dilute Hydrogen plasma. Find the distance $s$ from pulsar to earth, given $\tau= t_2 - t_2$. See [[Fall_2012#Question_12| F'12Q12]] for solutions. </ins></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>'''Q2:''' Obtain the non-relativistic Larmor radiation equation from the relativistic one. (S'08Q10) &lt;div class=&quot;mw-collapsible mw-collapsed&quot; style=&quot;width:750px&quot;&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>'''Q2:''' Obtain the non-relativistic Larmor radiation equation from the relativistic one. (S'08Q10) &lt;div class=&quot;mw-collapsible mw-collapsed&quot; style=&quot;width:750px&quot;&gt;</div></td></tr> </table>

Tom Neiser https://physwiki.com/w/index.php?title=EM_Course_Notes&diff=10607&oldid=prev 2014-05-13T02:16:37Z

<p>‎<span dir="auto"><span class="autocomment">210B Notes</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black;">← Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 02:16, 13 May 2014</td> </tr><tr><td colspan="2" class="diff-lineno">Line 181:</td> <td colspan="2" class="diff-lineno">Line 181:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>===''&lt;small&gt;Exercises&lt;/small&gt;''===</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>===''&lt;small&gt;Exercises&lt;/small&gt;''===</div></td></tr> <tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>'''Q1:'''A pulsar emits bursts of radio waves at two frequencies $\omega_1$, $\omega_2$. The pulses arrive at different times $t_1$, $t_2$ due to interaction with the interstellar medium- a dilute Hydrogen plasma. Find the distance $s$ from pulsar to earth, given $\tau= t_2 - t_2$. (F'12Q12)&lt;div class=&quot;mw-collapsible mw-collapsed&quot; style=&quot;width:750px&quot;&gt;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>'''Q1:''' A pulsar emits bursts of radio waves at two frequencies $\omega_1$, $\omega_2$. The pulses arrive at different times $t_1$, $t_2$ due to interaction with the interstellar medium- a dilute Hydrogen plasma. Find the distance $s$ from pulsar to earth, given $\tau= t_2 - t_2$. (F'12Q12)&lt;div class=&quot;mw-collapsible mw-collapsed&quot; style=&quot;width:750px&quot;&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>See [[Fall_2012#Question_12| F'12Q12]]. &#160;</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>See [[Fall_2012#Question_12| F'12Q12]]. &#160;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>&lt;/div&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>&lt;/div&gt;</div></td></tr> </table>

Tom Neiser https://physwiki.com/w/index.php?title=EM_Course_Notes&diff=10606&oldid=prev 2014-05-13T02:16:09Z

<p>‎<span dir="auto"><span class="autocomment">210B Notes</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black;">← Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 02:16, 13 May 2014</td> </tr><tr><td colspan="2" class="diff-lineno">Line 181:</td> <td colspan="2" class="diff-lineno">Line 181:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>===''&lt;small&gt;Exercises&lt;/small&gt;''===</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>===''&lt;small&gt;Exercises&lt;/small&gt;''===</div></td></tr> <tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>A pulsar emits bursts of radio waves at two frequencies $\omega_1$, $\omega_2$. The pulses arrive at different times $t_1$, $t_2$ due to interaction with the interstellar medium- a dilute Hydrogen plasma. Find the distance $s$ from pulsar to earth, given $\tau= t_2 - t_2$. (F'12Q12)&lt;div class=&quot;mw-collapsible mw-collapsed&quot; style=&quot;width:750px&quot;&gt;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">'''Q1:'''</ins>A pulsar emits bursts of radio waves at two frequencies $\omega_1$, $\omega_2$. The pulses arrive at different times $t_1$, $t_2$ due to interaction with the interstellar medium- a dilute Hydrogen plasma. Find the distance $s$ from pulsar to earth, given $\tau= t_2 - t_2$. (F'12Q12)&lt;div class=&quot;mw-collapsible mw-collapsed&quot; style=&quot;width:750px&quot;&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>See [[Fall_2012#Question_12| F'12Q12]]. &#160;</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>See [[Fall_2012#Question_12| F'12Q12]]. &#160;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>&lt;/div&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>&lt;/div&gt;</div></td></tr> <tr><td colspan="2" class="diff-lineno">Line 187:</td> <td colspan="2" class="diff-lineno">Line 187:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Obtain the non-relativistic Larmor radiation equation from the relativistic one. (S'08Q10) &lt;div class=&quot;mw-collapsible mw-collapsed&quot; style=&quot;width:750px&quot;&gt;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">'''Q2:''' </ins>Obtain the non-relativistic Larmor radiation equation from the relativistic one. (S'08Q10) &lt;div class=&quot;mw-collapsible mw-collapsed&quot; style=&quot;width:750px&quot;&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>From [http://en.wikipedia.org/wiki/Larmor_formula Wikipedia]:</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>From [http://en.wikipedia.org/wiki/Larmor_formula Wikipedia]:</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>:&lt;math&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>:&lt;math&gt;</div></td></tr> </table>

Tom Neiser https://physwiki.com/w/index.php?title=EM_Course_Notes&diff=10605&oldid=prev 2014-05-13T02:15:17Z

<p>‎<span dir="auto"><span class="autocomment">210B Notes</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black;">← Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 02:15, 13 May 2014</td> </tr><tr><td colspan="2" class="diff-lineno">Line 209:</td> <td colspan="2" class="diff-lineno">Line 209:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>See [[Spring_2008#Question_10| S'08Q10]]. &#160;</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>See [[Spring_2008#Question_10| S'08Q10]]. &#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&lt;/div&gt;</ins></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>&lt;br/&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>&lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> </table>

Tom Neiser https://physwiki.com/w/index.php?title=EM_Course_Notes&diff=10604&oldid=prev 2014-05-13T02:14:30Z

<p>‎<span dir="auto"><span class="autocomment">210B Notes</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black;">← Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 02:14, 13 May 2014</td> </tr><tr><td colspan="2" class="diff-lineno">Line 187:</td> <td colspan="2" class="diff-lineno">Line 187:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Obtain the non-relativistic Larmor radiation equation from the relativistic one<del class="diffchange diffchange-inline">.&#160; Click &lt;nowiki&gt; [Expand]&lt;/nowiki&gt; to see the solution</del>. (S'08Q10) &lt;div class=&quot;mw-collapsible mw-collapsed&quot; style=&quot;width:750px&quot;&gt;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Obtain the non-relativistic Larmor radiation equation from the relativistic one. (S'08Q10) &lt;div class=&quot;mw-collapsible mw-collapsed&quot; style=&quot;width:750px&quot;&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>From [http://en.wikipedia.org/wiki/Larmor_formula Wikipedia]:</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>From [http://en.wikipedia.org/wiki/Larmor_formula Wikipedia]:</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>:&lt;math&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>:&lt;math&gt;</div></td></tr> </table>

Tom Neiser https://physwiki.com/w/index.php?title=EM_Course_Notes&diff=10603&oldid=prev 2014-05-13T02:14:08Z

<p>‎<span dir="auto"><span class="autocomment">210B Notes</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black;">← Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 02:14, 13 May 2014</td> </tr><tr><td colspan="2" class="diff-lineno">Line 181:</td> <td colspan="2" class="diff-lineno">Line 181:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>===''&lt;small&gt;Exercises&lt;/small&gt;''===</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>===''&lt;small&gt;Exercises&lt;/small&gt;''===</div></td></tr> <tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">Fall 2012 Q12: </del>A pulsar emits bursts of radio waves at two frequencies $\omega_1$, $\omega_2$. The pulses arrive at different times $t_1$, $t_2$ due to interaction with the interstellar medium- a dilute Hydrogen plasma. Find the distance $s$ from pulsar to earth, given $\tau= t_2 - t_2$.&lt;div class=&quot;mw-collapsible mw-collapsed&quot; style=&quot;width:750px&quot;&gt;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>A pulsar emits bursts of radio waves at two frequencies $\omega_1$, $\omega_2$. The pulses arrive at different times $t_1$, $t_2$ due to interaction with the interstellar medium- a dilute Hydrogen plasma. Find the distance $s$ from pulsar to earth, given $\tau= t_2 - t_2$. <ins class="diffchange diffchange-inline">(F'12Q12)</ins>&lt;div class=&quot;mw-collapsible mw-collapsed&quot; style=&quot;width:750px&quot;&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>See [[Fall_2012#Question_12| F'12Q12]]. &#160;</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>See [[Fall_2012#Question_12| F'12Q12]]. &#160;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>&lt;/div&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>&lt;/div&gt;</div></td></tr> <tr><td colspan="2" class="diff-lineno">Line 187:</td> <td colspan="2" class="diff-lineno">Line 187:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">Spring 2008 Q10: </del>Obtain the non-relativistic Larmor radiation equation from the relativistic one.&#160; Click &lt;nowiki&gt; [Expand]&lt;/nowiki&gt; to see the solution. (S'08Q10) &lt;div class=&quot;mw-collapsible mw-collapsed&quot; style=&quot;width:<del class="diffchange diffchange-inline">800px</del>&quot;&gt;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Obtain the non-relativistic Larmor radiation equation from the relativistic one.&#160; Click &lt;nowiki&gt; [Expand]&lt;/nowiki&gt; to see the solution. (S'08Q10) &lt;div class=&quot;mw-collapsible mw-collapsed&quot; style=&quot;width:<ins class="diffchange diffchange-inline">750px</ins>&quot;&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>From [http://en.wikipedia.org/wiki/Larmor_formula Wikipedia]:</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>From [http://en.wikipedia.org/wiki/Larmor_formula Wikipedia]:</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>:&lt;math&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>:&lt;math&gt;</div></td></tr> </table>

Tom Neiser https://physwiki.com/w/index.php?title=EM_Course_Notes&diff=10602&oldid=prev 2014-05-13T02:13:02Z

<p>‎<span dir="auto"><span class="autocomment">210B Notes</span></span></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black;">← Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 02:13, 13 May 2014</td> </tr><tr><td colspan="2" class="diff-lineno">Line 181:</td> <td colspan="2" class="diff-lineno">Line 181:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>===''&lt;small&gt;Exercises&lt;/small&gt;''===</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>===''&lt;small&gt;Exercises&lt;/small&gt;''===</div></td></tr> <tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>A pulsar emits bursts of radio waves at two frequencies $\omega_1$, $\omega_2$. The pulses arrive at different times $t_1$, $t_2$ due to interaction with the interstellar medium- a dilute Hydrogen plasma. Find the distance $s$ from pulsar to earth, given $\tau= t_2 - t_2$.&lt;div class=&quot;mw-collapsible mw-collapsed&quot; style=&quot;width:750px&quot;&gt;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">Fall 2012 Q12: </ins>A pulsar emits bursts of radio waves at two frequencies $\omega_1$, $\omega_2$. The pulses arrive at different times $t_1$, $t_2$ due to interaction with the interstellar medium- a dilute Hydrogen plasma. Find the distance $s$ from pulsar to earth, given $\tau= t_2 - t_2$.&lt;div class=&quot;mw-collapsible mw-collapsed&quot; style=&quot;width:750px&quot;&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>See [[Fall_2012#Question_12| F'12Q12]]. &#160;</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>See [[Fall_2012#Question_12| F'12Q12]]. &#160;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>&lt;/div&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>&lt;/div&gt;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Spring 2008 Q10: Obtain the non-relativistic Larmor radiation equation from the relativistic one.&#160; Click &lt;nowiki&gt; [Expand]&lt;/nowiki&gt; to see the solution. (S'08Q10) &lt;div class=&quot;mw-collapsible mw-collapsed&quot; style=&quot;width:800px&quot;&gt;</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">From [http://en.wikipedia.org/wiki/Larmor_formula Wikipedia]:</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">:&lt;math&gt;</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">P = \frac{2}{3}\frac{q^2}{c^3m^2}\left(\frac{d\vec{p}}{dt}\cdot\frac{d\vec{p}}{dt}\right).</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&lt;/math&gt;</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Assume the generalisation;</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">:&lt;math&gt;</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">P = -\frac{2}{3}\frac{q^2}{m^2c^3}\frac{dP^{\mu}}{d\tau}\frac{dP_{\mu}}{d\tau}.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&lt;/math&gt;</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">When we expand and rearrange the energy-momentum four vector product we get:</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">:&lt;math&gt;</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\frac{dP^{\mu}}{d\tau}\frac{dP_{\mu}}{d\tau} = \frac{v^2}{c^2}\left(\frac{dp}{d\tau}\right)^2 - \left(\frac{d\vec{p}}{d\tau}\right)^2</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&lt;/math&gt;</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">where I have used the fact that </ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">:&lt;math&gt; \frac{dE}{d\tau} = \frac{pc^2}{E}\frac{dp}{d\tau} = v\frac{dp}{d\tau} &lt;/math&gt;</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">When you let &lt;math&gt;\beta&lt;/math&gt; tend to zero, &lt;math&gt;\gamma&lt;/math&gt; tends to one, so that &lt;math&gt;d\tau&lt;/math&gt; tends to dt. Thus we recover the non relativistic case.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">See [[Spring_2008#Question_10| S'08Q10]]. </ins></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>&lt;br/&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>&lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> </table>

Tom Neiser