Question

A conducting sphere A of radius $a$, with charge $Q$ is placed concentrically inside a conducting shell $B$ of radius $b$. $B$ is earthed, $C$ is the common centre of $A$ and $B$ at distance $r$ from center $C,$ then which of the option(s) are correct.
use: $a=1\text{m},b=3\text{m},r=2\text{m}$ and $k=\frac{1}{4\pi {ϵ}_0},V_{\infty }=0$

• A. Electric field at point P is $\frac{kQ}{4}$
• B. Electric potential at point P is $\frac{kQ}{3}$
• C. Electric potential difference between A and B is $\frac{2KQ}{3}$
• D. Electric field outside the shell B zero

Answer 1

Answer: (A), (C), (D)

Electric field outside the shell B zero

Due to earthing redistribution of charges can be considered as


Using Gauss law $E_p=\frac{KQ}{r^2}=\frac{KQ}{4}$
Potential of point $P$$=\frac{KQ}{r}+\frac{K(-Q)}{b}$
=$\frac{KQ}{2}+\frac{K(-Q)}{3}$
=$\frac{KQ}{6}$
Potential difference between spheres is $P$$=\frac{KQ}{a}+\frac{K(-Q)}{b}-0$
$=\frac{KQ}{1}+\frac{K(-Q)}{3}$
$=\frac{2KQ}{3}$
For any point outside, applying GaUss law $E=0$