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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
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The correct answer is:
zero
Flux through surface $A$,
$\begin{aligned} & \phi_A=E \times \pi R^2 \\ & \phi_B=-E \times \pi R^2\end{aligned}$
Flux through curved surface, $C=\int E \cdot d S$
$=\int E d S \cos 90^{\circ}=0$
$\therefore$ Total flux through cylinder $=\phi_A+\phi_B+\phi_C=0$
$\begin{aligned} & \phi_A=E \times \pi R^2 \\ & \phi_B=-E \times \pi R^2\end{aligned}$
Flux through curved surface, $C=\int E \cdot d S$
$=\int E d S \cos 90^{\circ}=0$
$\therefore$ Total flux through cylinder $=\phi_A+\phi_B+\phi_C=0$
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