Question

A point charge +$q$ is placed on the axis of a closed cylinder of radius $R$ and height $\frac{25R}{12}$ as shown. If electric flux coming out form the curved surface of cylinder is $\frac{xq}{10{\in }_0}$, then calculate $x$.

Answer 1

$\varphi =\frac{q}{{\in }_0}-\frac{q}{{\in }_0}\left(\frac{2\pi (1-\cos {37}^{\circ }}{4\pi }\right)-\frac{q}{{\in }_0}\left(\frac{2\pi (1-\cos {53}^{\circ }}{4\pi }\right)$
$\varphi =\frac{q}{{\in }_0}[1-\frac{1}{2}(1-\frac{4}{5})-\frac{1}{2}(1-\frac{3}{5})]$
$\frac{q}{{\in }_0}[1-\frac{1}{10}-\frac{2}{10}]=\frac{7q}{10{\in }_0}$