frac {q} {2\gamma m} (B_z -\frac {\psi_0} {\pi r}).\]</div>
<p>Exclude <span class="math notranslate nohighlight">\(\dot\theta\)</span> and substitute <span class="math notranslate nohighlight">\(\displaystyle\dot\gamma\approx\frac {\beta q E_z} {mc}:\)</span></p>
<div class="math notranslate nohighlight">
\[\ddot r +\frac {\beta q E_z} {\gamma mc}\dot r +\frac {q ^ 2 B ^ 2_z} {4\gamma ^ 2 m ^ 2} r -\frac {q ^ 2\psi ^ 2_0} {4\pi ^ 2\gamma ^ 2 m ^ 2} (\frac {1} {r ^ 3}) -\frac {q E_r} {\gamma m} = 0.\]</div>