Question

Two concentric spherical shell of radii a, b (a < b) has charge q and -q respectively. Electric field does exist -

• A. Inside inner sphere only
• B. Outside outer sphere only
• C. between two shells only
• D. Everywhere is zero

Answer 1

Answer: (C)

between two shells only

Answer 2

The electric field exists only between the two shells. This is because:

1. For r < a: No charge is enclosed (Gaussian surface inside the inner shell). Hence, E = 0.

2. For a < r < b: Only the inner shell with charge q is enclosed. By Gauss's law:

   $$E \cdot 4\pi r^2 = \frac{q}{\epsilon_0} \implies E = \frac{q}{4\pi \epsilon_0 r^2}$$

   Thus, E ≠ 0.

3. For r > b: The net enclosed charge is q + (-q) = 0. Hence, E = 0.