Question

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

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

Answer 1

The correct option is not present. It should be zero.
Flux through surface A ${\varphi }_A=E\times \pi R^{2}and{\varphi }_B=-E\times \pi R^2$

Flux through curved surface $C=\int \dot{E}.\dot{ds}=\int Edscos{90}^{\circ }=0$
$\therefore$ Total flux through cylinder $={\varphi }_A+{\varphi }_B+{\varphi }_C=0$