Question

The electric field inside a uniformly charged spherical shell of radius \( R \) is:

• A. directly proportional to the charge within the shell
• B. inversely proportional to \( R^2 \)
• C. same as that outside the shell
• D. zero
• E. maximum at the centre

Hint:

Inside a uniformly charged spherical shell, the electric field is always zero. This is a direct consequence of Gauss’s law and the symmetry of the problem.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
According to Gauss's Law, the total electric flux through any closed surface is proportional to the enclosed electric charge. For a spherical shell, we consider a Gaussian surface inside the shell.
Step 2: Detailed Explanation
1. A uniformly charged spherical shell has all its charge distributed on its outer surface. 2. If we take a Gaussian sphere of radius \(r<R\) (inside the shell), the total charge enclosed (\(q_{enclosed}\)) is exactly zero. 3. Applying Gauss's Law: \[ \oint E \cdot dA = \frac{q_{enclosed}}{\epsilon_0} \] 4. Since \(q_{enclosed} = 0\), the electric field \(E\) must be zero at all points inside the shell.
Step 3: Final Answer
The electric field inside the shell is zero.