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An electric charge $q$ is placed at the centre of a cube of side $a$. The electric flux through one face of the cube will be

1. $\frac{q}{6\epsilon_0}$
2. $\frac{2q}{a\epsilon_0}$
3. $\frac{2q}{4\pi a^2\epsilon_0}$
4. $\frac{q}{\epsilon_0}$

Correct answer: $\frac{q}{6\epsilon_0}$

Solution

By Gauss's law, the total electric flux through the cube is $q/\epsilon_0$. Since the charge is at the center, symmetry implies equal flux through all 6 faces. Therefore, flux through one face is $q/(6\epsilon_0)$.

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