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 $B$. If $P$ is the point between shells $A$ and $B$ at distance $r$ from center $C$ then Match the proper entries from column- 2 to column- 1 using the codes given below the columns, (use $a=1m,b=3m,r=2m\text{and}K=\frac{1}{4\pi {\epsilon }_0})$

Column-I	Column-II
(p) Electric field at point $P$ is	(1) $\frac{2KQ}{3}$
(q) Electric potential at point $P$ is	(2) zero
(r) Electric potential difference between $A$ and $B$ is	(3) $\frac{KQ}{4}$
(s) Electric field outside the shell $B$ at distance $5m$ from centre $C$ is	(4) $\frac{KQ}{6}$

• A. p-4; q-2; r-1; s-3
• B. p-1; q-2; r-4; s-3
• C. p-2; q-3; r-4; s-1
• D. p-3; q-4; r-1; s-2

Answer 1

The correct option is D p-3; q-4; r-1; s-2


Field at $P$ will only be due to A as electric field inside the conducting sphere B will be zero.
$\therefore$ $E_P$ $=\frac{kQ}{(2{)}^2}=\frac{kQ}{4}$
Potential at $P=V_{\text{due to A}}+V_{\text{due to B}}=\frac{kQ}{2}-\frac{kQ}{3}$
Electric field outside $B$ is due to 'A's Induced charge on $B+A^{\prime }$ s charge.
$⟹$ $E_{outside}=\frac{kQ}{5^2}-\frac{kQ}{5^2}$= $0$