A point charge Q is kept at the midpoint of a face of cube of side L. The electric flux emerging from the cube is

$Q (2ε_0)^{-1}$

The correct answer is Option (4) → $Q (2ε_0)^{-1}$

Given:

Point charge $Q$ placed at the midpoint of one face of a cube of side $L$.

Concept:

According to Gauss’s law, total flux due to a point charge $Q$ through a closed surface enclosing it completely is

$\Phi_{total} = \frac{Q}{\varepsilon_0}$

Here, the charge lies on the face of the cube, not inside it. If identical cubes are imagined around the charge such that the charge lies at the common face center, it will be shared by two cubes.

Thus, flux through one cube = $\frac{1}{2}$ of the total flux.

Calculation:

$\Phi = \frac{1}{2} \cdot \frac{Q}{\varepsilon_0}$

Final Answer:

Electric flux emerging from the cube = $\frac{Q}{2\varepsilon_0}$