Question

An electric charge \( q \) is placed at the centre of a cube of side \( l \). The electric flux through one of its faces will be

• A. \( \frac{q}{\epsilon_0} \)
• B. \( \frac{q}{6 \epsilon_0} \)
• C. \( \frac{q}{\epsilon_0} \cdot \frac{1}{4 \pi l^2} \)
• D. \( \frac{q}{4 \pi \epsilon_0 l^2} \)

Hint:

Gauss's law helps in calculating the electric flux through a closed surface. When the charge is at the center, the flux is equally distributed through all faces of the surface.

Answer 1

The Correct Option is B

Gauss's law states that the electric flux \( \Phi_E \) through a closed surface is given by: \[ \Phi_E = \frac{q_{{enclosed}}}{\epsilon_0} \] When the charge \( q \) is placed at the center of the cube, the total flux is \( \frac{q}{\epsilon_0} \). Since the cube has 6 faces, the flux through each face will be equally distributed. Therefore, the flux through one face is: \[ \frac{q}{6 \epsilon_0} \] Hence, the correct answer is (b).