http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?action=history&feed=atom&title=Magnetic_mirror_%2F_electron_motion_and_velocity 2026-07-23T16:45:43Z Histórico de edições para esta página nesta wiki MediaWiki 1.35.2 http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?title=Magnetic_mirror_/_electron_motion_and_velocity&diff=3360&oldid=prev 2017-06-17T15:58:36Z

<p></p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="pt"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Revisão anterior</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revisão das 15h58min de 17 de junho de 2017</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Linha 1:</td> <td colspan="2" class="diff-lineno">Linha 1:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>(F. F. ~ Chen 2.20)</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>(F. F. ~ Chen 2.20)</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The magnetic field along the axis of a magnetic mirror is \(B_(z) = B_0(1+\alpha^2z^2)\), where \(\alpha\) is</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The magnetic field along the axis of a magnetic mirror is \(B_(z) = B_0(1+\alpha^2z^2)\), where \(\alpha\) is</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>a constant. Suppose that at <del class="diffchange diffchange-inline">$</del>z=0<del class="diffchange diffchange-inline">$ </del>an electron has velocity \(v^2 = 3 v_{\parallel}^2 = \frac{3}{2}v_{\perp}^2\).</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>a constant. Suppose that at <ins class="diffchange diffchange-inline">\(</ins>z=0<ins class="diffchange diffchange-inline">\) </ins>an electron has velocity \(v^2 = 3 v_{\parallel}^2 = \frac{3}{2}v_{\perp}^2\).</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>(a) Describe qualitatively the electron motion.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>(a) Describe qualitatively the electron motion.</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>(b) Determine the values of <del class="diffchange diffchange-inline">$</del>z<del class="diffchange diffchange-inline">$ </del>where the electron is reflected.</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>(b) Determine the values of <ins class="diffchange diffchange-inline">\(</ins>z<ins class="diffchange diffchange-inline">\) </ins>where the electron is reflected.</div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>(c) Write the equation of motion of the guiding center for the direction parallel to \(\vec{B}\) and show that there is a</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>(c) Write the equation of motion of the guiding center for the direction parallel to \(\vec{B}\) and show that there is a</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>sinusoidal oscillation. Calcule the frequency of the motion as a function of \(v\).</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>sinusoidal oscillation. Calcule the frequency of the motion as a function of \(v\).</div></td></tr> </table>

Ist426982 http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?title=Magnetic_mirror_/_electron_motion_and_velocity&diff=3358&oldid=prev 2017-06-17T15:58:03Z

<p>Criou a página com &quot;(F. F. ~ Chen 2.20) The magnetic field along the axis of a magnetic mirror is \(B_(z) = B_0(1+\alpha^2z^2)\), where \(\alpha\) is a constant. Suppose that at $z=0$ an electr...&quot;</p> <p><b>Página nova</b></p><div>(F. F. ~ Chen 2.20)<br /> The magnetic field along the axis of a magnetic mirror is \(B_(z) = B_0(1+\alpha^2z^2)\), where \(\alpha\) is<br /> a constant. Suppose that at $z=0$ an electron has velocity \(v^2 = 3 v_{\parallel}^2 = \frac{3}{2}v_{\perp}^2\).<br /> <br /> (a) Describe qualitatively the electron motion.<br /> (b) Determine the values of $z$ where the electron is reflected.<br /> (c) Write the equation of motion of the guiding center for the direction parallel to \(\vec{B}\) and show that there is a<br /> sinusoidal oscillation. Calcule the frequency of the motion as a function of \(v\).</div>

Ist426982