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 states that the net electric flux through any closed surface is proportional to the net electric charge enclosed by that surface (\( \Phi_E = \oint \vec{E} \cdot d\vec{A} = \frac{Q_{enc}}{\epsilon_0} \)).

Step 2: Consider a Gaussian surface inside the hollow conductor. For a hollow spherical conductor, any charge placed on it will reside entirely on its outer surface due to electrostatic repulsion. If we draw a spherical Gaussian surface at any radius \(r\) inside the hollow conductor, this surface encloses no charge (\(Q_{enc} = 0\)).

Step 3: Conclude the value of the electric field. Since \(Q_{enc} = 0\), Gauss's Law gives: \[ \oint \vec{E} \cdot d\vec{A} = 0 \] Due to the spherical symmetry, the electric field \(E\) must be constant in magnitude on the Gaussian surface and directed radially. Therefore, the integral becomes \( E \cdot (4\pi r^2) = 0 \). Since the area \(4\pi r^2\) is not zero, the electric field \(E\) must be zero everywhere inside the conductor.