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   [NEET 2014]

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]

\[{{E}_{\text{inside}}}=0\]

and       \[{{V}_{\text{inside}}}={{V}_{\text{surface}}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{Q}{R}\]