Question

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 $\frac{Q}{4\pi {\epsilon }_0{R}^2}$
• B. $\frac{Q}{4\pi {\epsilon }_{0}R}$ and Zero
• C. $\frac{Q}{4\pi {\epsilon }_{0}R}$ and $\frac{Q}{4\pi {\epsilon }_0{R}^2}$
• D. Both are Zero

Answer 1

Answer: (B)

For the conducting sphere,
Potential at the centre = Potential on the sphere
$=\frac{1}{4\pi {\epsilon }_0}\frac{Q}{R}$
Electric field at the centre = 0