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 center of $A$ and $B$. Study the following statements.
i. The potential at a distance $r$ from $C$, where
$a\le r\le b$, is $\frac{1}{4\pi {\epsilon }_0}\left(\frac{Q}{r}\right)$
ii. The potential difference between $A$ and $B$ is
$\frac{1}{4\pi {\epsilon }_0}Q\left(\frac{1}{a}-\frac{1}{b}\right)$
iii. The potential at a distance $r$ from $C$, where
$a\le r\le b,$ is $\frac{1}{4\pi {\epsilon }_0}Q\left(\frac{1}{r}-\frac{1}{b}\right)$
Which of the following statements are correct?

• A. Only (i) and (ii)
• B. Only (ii) and (iii)
• C. Only (i) and (iii)
• D. All

Answer 1

Answer: (B)

Charge $+Q$ will flow into earth.
$V_C=\frac{kQ}{r}-\frac{kQ}{b}$
$V_A=\frac{kQ}{a}-\frac{kQ}{b}$
Potential at $B$ is zero.