Trajectory equation for one particle<a class="headerlink" href="#Trajectory-equation-for-one-particle" title="Permalink to this headline">¶</a></h2>
<p>The vector potential in the solenoid has only one component and is easily expressed in terms of <span class="math notranslate nohighlight">\(B_z (z)\)</span>:</p>
<div class="math notranslate nohighlight">
\[A_ \phi (z, r) = \sum_0 ^ {inf} \dfrac {(- 1) ^ n} {n! (N + 1)!} B_z ^ {2n} (\dfrac {r} {2}) ^ {2n + 1/2}.\]</div>
<p>Therefore, the Lagrangian in a cy