epsilon_y\beta_y}.\]</div>
<p>The field is obtained linearly inside the charged elliptical cylinder:</p>
<div class="math notranslate nohighlight">
\[E_x =\displaystyle\frac {4I} {\upsilon}\frac {x} {a (a + b)},\]</div>
<div class="math notranslate nohighlight">
\[E_y =\displaystyle\frac {4I} {\upsilon}\frac {y} {b (a + b)}.\]</div>
<p>Check that <span class="math notranslate nohighlight">\(\nabla\vec {E} = 4\pi\rho:\)</span></p>
<div class="math notranslate nohighlight">
\[\displaystyle I =\rho\upsilon\pi 