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. Gauss's Law Application:
A charge \( q \) positioned at the center of a cube's face distributes its influence equally to two adjoining cubes.
2. Flux Determination:
Gauss's law states that the total flux \( \Phi \) from a charge \( q \) through a closed surface is:
\[ \Phi_{\text{total}} = \frac{q}{\epsilon_0}. \] As the charge \( q \) is equally shared by two adjacent cubes, the flux experienced by each cube is:
\[ \Phi = \frac{q}{2\epsilon_0}. \]

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