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

The Correct Option is B

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: \( \frac{q}{2\epsilon_0} \)