Question

A conducting sphere of radius R is charged to a potential of V volt. Then the electric field at a distance \(r(>R)\) from the centre of sphere would be :

• A. \( \frac{RV}{r^2} \)
• B. \( \frac{V}{r} \)
• C. \( \frac{rV}{R^2} \)
• D. \( \frac{R^2V}{r^3} \)

Hint:

Outside a charged sphere, it behaves like a point charge at centre.

Answer 1

The Correct Option is A

Concept: Potential of sphere: \[ V = \frac{kQ}{R} \Rightarrow Q = \frac{VR}{k} \] Electric field: \[ E = \frac{kQ}{r^2} \]

Step 1: Substitute Q.
\[ E = \frac{k \cdot (VR/k)}{r^2} = \frac{RV}{r^2} \]