A point charge of 17.7 μC is located at the center of a cube of side 0.03 m. Find the electric flux through each face of the cube.

$3.3 × 10^5\, Nm^2C^{-1}$

The correct answer is Option (1) → $3.3 × 10^5\, Nm^2C^{-1}$

Given:

Charge, $ q = 17.7\ \mu C = 17.7 \times 10^{-6}\ \text{C} $

Side of cube, $ a = 0.03\ \text{m} $

By Gauss’s law:

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

where $ \varepsilon_0 = 8.854 \times 10^{-12}\ \text{C}^2/\text{N·m}^2 $

$ \Phi_{total} = \frac{17.7 \times 10^{-6}}{8.854 \times 10^{-12}} = 2.00 \times 10^{6}\ \text{N·m}^2/\text{C} $

The cube has 6 faces, and since the charge is at the centre, the flux is equally distributed.

Flux through each face:

$ \Phi_{face} = \frac{\Phi_{total}}{6} = \frac{2.00 \times 10^{6}}{6} = 3.33 \times 10^{5}\ \text{N·m}^2/\text{C} $

Therefore, the electric flux through each face of the cube is $ 3.33 \times 10^{5}\ \text{N·m}^2/\text{C} $.