Question

A metal sphere with 1 m radius and a surface charge density of $10 \,\text{C/m}^2$ is enclosed in a cube of side 1 m. The total outward electric displacement flux normal to the surface of the cube is:

• A. $5\pi$ coulombs
• B. $10\pi$ coulombs
• C. $20\pi$ coulombs
• D. $40\pi$ coulombs

Hint:

Flux depends only on enclosed charge, not shape of surface.

Answer 1

The Correct Option is D

Concept: According to Gauss’s Law: \[ \Phi = Q_{\text{enclosed}} \] Electric flux depends only on enclosed charge.

Step 1: Surface charge density relation \[ Q = \sigma \cdot A \]

Step 2: Surface area of sphere \[ A = 4\pi r^2 = 4\pi (1)^2 = 4\pi \]

Step 3: Total charge \[ Q = 10 \times 4\pi = 40\pi \]

Step 4: Apply Gauss law Flux through cube = total enclosed charge \[ \Phi = 40\pi \] \[ \therefore \text{Correct answer is (D)} \]