A Gaussian surface in the cylinder of cross section ${}^{'}{π {a^{2}}^{'}}$ and length ‘L’ is immersed in a uniform electric field $\vec{E}$ with the cylinder axis parallel to the field. The flux ${}^{'}ϕ^{'}$ of the electric field through the closed surface is

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$2 π a^{2} \vec{E}$

$π a^{2} \vec{E} L$

$π a^{2} (2 + L) \vec{E}$

Zero

answer is D.

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Detailed Solution

The electric lines of force would enter from one surface of the cylinder and leave out from the other. Thus the net flux through the cylinder would be: $\vec{B} . {\vec{A}}_{1} + \vec{B} . {\vec{A}}_{2}$

$B (π a^{2}) + B (- π a^{2}) = 0$

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