Question

A conducting sphere of radius ' $\text{R}$ ' is given a charge ' $Q$ ' uniformly. The electric field and the electric potential at the centre of the sphere are respectively [ $\varepsilon_0 =$ permittivity of free space]}

• A. zero and $\frac{Q}{4\pi\varepsilon_0 R}$
• B. $\frac{\text{Q}}{4\pi\varepsilon_0 \text{R}^2}$ and zero
• C. $\frac{\text{Q}}{4\pi\varepsilon_0 \text{R}}$ and $\frac{\text{Q}}{4\pi\varepsilon_0 \text{R}^2}$
• D. zero and zero

Hint:

Inside a hollow/conducting sphere: $E = 0$ but $V \neq 0$. The potential is "flat" like a tabletop across the interior.

Answer 1

The Correct Option is A

Step 1: Concept
For a charged conducting sphere, all charge resides on the outer surface.

Step 2: Meaning
Inside a conductor, the electric field ($E$) is always zero because there are no enclosed charges.

Step 3: Analysis
Since $E = -\frac{dV}{dr} = 0$, the potential ($V$) must be constant everywhere inside and equal to the value at the surface.
$V_{center} = V_{surface} = \frac{Q}{4\pi\varepsilon_0 R}$.

Step 4: Conclusion
Electric field is zero and potential is $\frac{Q}{4\pi\varepsilon_0 R}$. Final Answer: (A)