Question

A cylinder of radius $R$ and length $L$ is placed in a uniform electric field $E$ parallel to the cylinder axis. The total flux for the surface of the cylinder is given by :

• A. $2\pi R^{2}E$
• B. $\frac{\pi R^2}{E}$
• C. $\frac{R}{E}$
• D. Zero

Answer 1

The correct option is D Zero

Flux through surface $A$,
${\varphi }_A=E\times \pi R^2$
${\varphi }_B=-E\times \pi R^2$
Flux through curved surface, $C=\int E.ds$
$=\int Eds\cos {90}^o=0$
$\therefore$ Total flux through cylinder $={\varphi }_A+{\varphi }_B+{\varphi }_C=0$