Question

Three concentric conducting spherical shells of radii $R,2R$ and $3R$ carry charges $Q,-2Q$ and $3Q$, respectively. Find the electric potential at $r=R$ and $r=3R$, where $r$ is the radial distance from the centre.

• A. $\frac{Q}{6\pi {\epsilon }_{0}R},\frac{Q}{4\pi {\epsilon }_{0}R}$
• B. $\frac{Q}{4\pi {\epsilon }_{0}R},\frac{Q}{6\pi {\epsilon }_{0}R}$
• C. $\frac{Q}{2\pi {\epsilon }_{0}R},\frac{Q}{3\pi {\epsilon }_{0}R}$
• D. $\frac{Q}{3\pi {\epsilon }_{0}R},\frac{Q}{2\pi {\epsilon }_{0}R}$

Answer 1

Answer: (B)

$\frac{Q}{4\pi {\epsilon }_{0}R},\frac{Q}{6\pi {\epsilon }_{0}R}$

Potential at $r=R$
$V\left(r\right)=\frac{Q}{4\pi {ϵ}_{0}R}$

Potential at $r=3R$
$V\left(r\right)=\frac{Q}{4\pi {ϵ}_{0}3R}+\frac{-2Q}{4\pi {ϵ}_{0}3R}+\frac{3Q}{4\pi {ϵ}_{0}3R}=\frac{Q}{6\pi {ϵ}_{0}R}$