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Eight point charges (can be assumed as small spheres uniformly charged and their centers at the corner of the cube) having values q each are fixed at vertices of a cube. The electric flux through square surface ABCD of the cube is

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$\frac{q}{24 \in_{0}}$

$\frac{q}{12 \in_{0}}$

$\frac{q}{6 \in_{0}}$

$\frac{q}{8 \in_{0}}$

answer is C.

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Detailed Solution

The electric flux through ABCD due to charges at A, B, C and D is zero.

The flux through ABCD due to any of the charges at E, F, G& H
are $\frac{q}{24 \in_{0}}$ each.
Hence the net electric flux through ABCD is $ϕ = 4 \times 0 + 4 \times \frac{q}{24 \in_{0}} = \frac{q}{6 \in_{0}}$

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