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 [AIPMT 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 :

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