Question

Inside a uniformly charged spherical shell, the value of the electric field at distance r from the center is:

• A. 0
• B. kQ/r
• C. kQ/r\(^2\)
• D. Constant

Hint:

This is a classic result of Gauss's Law. It also applies to the inside of any hollow conductor in electrostatic equilibrium, a principle used in Faraday cages for electrostatic shielding.

Answer 1

The Correct Option is A

Step 1: Apply Gauss's Law within the shell. Use a spherical Gaussian surface of radius \(r\) (where \(r\)<shell radius), concentric with the charged shell. Gauss's Law: Net electric flux = enclosed charge / \(\epsilon_0\). \[ \oint \vec{E} \cdot d\vec{A} = \frac{Q_{enclosed}}{\epsilon_0} \]
Step 2: Determine the enclosed charge. Charge on a spherical shell is on its surface. A Gaussian surface inside the shell (radius \(r\)) encloses no charge. \[ Q_{enclosed} = 0 \]
Step 3: Calculate the electric field. With \(Q_{enclosed} = 0\), the net flux is zero. \[ \oint \vec{E} \cdot d\vec{A} = 0 \] Spherical symmetry implies a constant electric field magnitude on the Gaussian surface. The integral is \(E \times (4\pi r^2)\). For this to be zero, \(E\) must be zero. \[ E = 0 \] Therefore, the electric field is zero everywhere inside a uniformly charged spherical shell.