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 from the surface of the cylinder is

• A. $2\pi R^{2}E$
• B. $\pi R^2/E$
• C. $(\pi R^2-\pi R)/E$
• D. Zero

Answer 1

The correct option is D Zero

The electric flux passing through a surface of area $A$ is $\phi =\overrightarrow{E}.\overrightarrow{A}$


Flux through surface $A$ is ${\phi }_A=E\times \pi R^2$
and
Flux through surface $B$ is ${\phi }_B=-E\times \pi R^2$

Flux through curved surface $C$ is
$\int \overrightarrow{E}.\overrightarrow{ds}=\int Eds\cos {90}^{\circ }=0$
$\therefore$ Total flux through cylinder ${\phi }_A+{\phi }_B+{\phi }_C=0$