Question

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

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

Answer 1

The correct option is B $\frac{Q}{4\pi {ϵ}_{0}R}$ and Zero

Electric field inside a conducting shell is zero. So, $E$ at center and potential remains constant at any point inside the shell.
Therefore $E=0\text{and}V=\frac{Q}{4\pi {ϵ}_{0}R}$