Question

The electric field at a point inside a charged hollow spherical conductor is:

• A. zero
• B. constant but not zero
• C. depends on the distance from centre
• D. depends on the charge on the conductor

Hint:

A key result from electrostatics: the electric field inside any static conductor (hollow or solid) is always zero. This is the principle behind electrostatic shielding, used in devices like Faraday cages.

Answer 1

The Correct Option is A

Step 1: Apply Gauss's Law. Gauss's Law relates electric flux to enclosed charge: \( \Phi_E = \oint \vec{E} \cdot d\vec{A} = \frac{Q_{enc}}{\epsilon_0} \).

Step 2: Consider a Gaussian surface within the hollow conductor. In a hollow spherical conductor, charge resides on the outer surface. A spherical Gaussian surface inside encloses no charge (\(Q_{enc} = 0\)).

Step 3: Determine the electric field. With \(Q_{enc} = 0\), Gauss's Law yields \[ \oint \vec{E} \cdot d\vec{A} = 0 \]. Due to symmetry, \(E\) is constant and radial. Thus, \( E \cdot (4\pi r^2) = 0 \). Since the area isn't zero, the electric field \(E\) is zero inside the conductor.