Question

The total charge on a uniformly charged spherical shell having radius R is Q. Then electric potential at a distance $r = R/2$ from the centre of the shell ______.

• A. $\frac{Q}{4\pi\varepsilon_0 R}$
• B. $\frac{Q}{\pi\varepsilon_0 R}$
• C. $\frac{Q}{2\pi\varepsilon_0 R}$
• D. $\frac{Q}{8\pi\varepsilon_0 R}$

Hint:

Remember: \textbf{Field} is zero inside, but \textbf{Potential} is constant (not zero) inside a hollow conductor.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
For a charged spherical shell, the electric field inside is zero. This means the electric potential remains constant at all points inside and is equal to the potential on the surface.
Step 2: Detailed Explanation:
The potential on the surface ($r=R$) is $V = \frac{Q}{4\pi\varepsilon_0 R}$. Since the potential is constant inside the shell ($0 \leq r \leq R$), the potential at $r = R/2$ is exactly the same as the potential on the surface. $$V_{inside} = \frac{Q}{4\pi\varepsilon_0 R}$$
Step 3: Final Answer:
The correct option is (a).