question_answer

A conducting sphere of radius R is given a charge Q. The electric potential and the electric field at the centre of the sphere respectively are:

A) zero and\[\frac{Q}{4\pi {{\varepsilon }_{0}}{{R}^{2}}}\]

B) \[\frac{Q}{4\pi {{\varepsilon }_{0}}R}\]and zero

C) \[\frac{Q}{4\pi {{\varepsilon }_{0}}R}\]and \[\frac{Q}{4\pi {{\varepsilon }_{0}}{{R}^{2}}}\]

D) Both are zero

Correct Answer: B

Solution :

(b) \[\frac{Q}{4\pi {{\varepsilon }_{0}}R}\]and zero \[{{E}_{inside}}=0\] And \[{{V}_{inside}}={{V}_{surface}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{Q}{R}\]