Question

A charge q is placed at the center of one of the surface of a cube. The flux linked with the cube is :-

• A. $\frac{q}{4\epsilon_0}$
• B. $\frac{q}{2\epsilon_0}$
• C. $\frac{q}{8\epsilon_0}$
• D. Zero

Answer 1

Answer: (B)

$\frac{q}{2\epsilon_0}$

Answer 2

1. Using Gauss’s Law:
When a charge $q$ is placed at the center of one face of a cube, it can be visualized that the charge $q$ contributes equally to two adjacent cubes.
2. Flux Calculation:
According to Gauss’s law, the total flux $\Phi$ due to charge $q$ in a closed surface is given by:
$\Phi_{\text{total}} = \frac{q}{\epsilon_0}.$ Since the charge $q$ is shared equally between two adjacent cubes, the flux through each cube is:
$\Phi = \frac{q}{2\epsilon_0}.$

Answer: $\frac{q}{2\epsilon_0}$