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1. Electric Charges and Fields
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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
$2 \pi R^2E$
B
$\pi R^2/E$
C
$(\pi R^2/ \pi R)/E$
D
zero
Solution

Flux through surface $A$
$\phi_{A}=E \times \pi R^{2}$
$\phi_{B}=-E \times \pi R^{2}$
Flux through curved surface, $C=\int E . d s$
$=\int E d s \cos 90^{\circ}=0$
$\therefore$ Total flux through cylinder $=\phi_{A}+\phi_{B}+\phi_{C}=0$
Standard 12
Physics
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