Question

$A$ and $C$ are concentric conducting spherical shells of radius 𝑎 and 𝑐 respectively. $A$ is surrounded by a concentric dielectric medium of inner radius $a$ , outer radius $b$ and dielectric constant $k$. If sphere $A$ is given a charge $Q$, the potential at the outer surface of the dielectric is

• A. None of these
• B. $\frac{Q}{4\pi {ϵ}_{0}kb}$
• C. $\frac{Q}{4\pi {ϵ}_0}(\frac{1}{a}-\frac{1}{k(b-a)})$
• D. $\frac{Q}{4\pi {ϵ}_{0}b}$

Answer 1

The correct option is D $\frac{Q}{4\pi {ϵ}_{0}b}$

since sphere $C$ is neutral

[induced Charge on outer surface of $C]=-[$induced Charge on inner surface of $C]$

Thus, potential at $B$ due to sphere

$C=0$

Also,

the dielectric is electrically neutral, so

[induced Charge on outer surface of dielectric] = -[induced charge on inner surface of dielectric]
potential at $B$ due to dielectric $=0$
hence, potential at $B$ is only due to charge of sphere $A$
Now, potential at 𝐵 due to charge on $A$
$=\frac{kQ}{b}=\frac{Q}{4\pi {ϵ}_{0}b}$
net potential at 𝐵
$=\frac{Q}{4\pi {ϵ}_{0}b}$
Hence, the correct option is (C).