Question 286 of 311

In a cuboid of dimension $2L\times 2L\times L$ , a charge $q$ is placed at the centre of the surface $S$ having area of $4{L}^{2}$ . The flux through the opposite surface to $S$ is given by

A$\dfrac{q}{12{\in }_{0}}$B$\dfrac{q}{3{\in }_{0}}$C$\dfrac{q}{2{\in }_{0}}$D$\dfrac{q}{6{\in }_{0}}$

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Answer: (D) $\dfrac{q}{6{\in }_{0}}$

Assume a similar cuboid on top of the given cuboid to make symmetry about charge. Thus, it becomes a cube of length $2L$.

Flux passing through whole cube is $\phi =\dfrac{q}{{\in }_{0}}$(Gauss's Law).
Since, total faces are $6$, so flux passing through shaded face $=\dfrac{q}{6{\in }_{0}}$.