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
$a \leq r \leq b$, is $\frac{1}{4 \pi \varepsilon_{0}}\left(\frac{Q}{r}\right)$
ii. The potential difference between $A$ and $B$ is
$\frac{1}{4 \pi \varepsilon_{0}} Q\left(\frac{1}{a}-\frac{1}{b}\right)$
iii. The potential at a distance $r$ from $C$, where
$a \leq r \leq b, $ is $ \frac{1}{4 \pi \varepsilon_{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{k Q}{r}-\frac{k Q}{b} $
$V_{A}=\frac{k Q}{a}-\frac{k Q}{b}$
Potential at $B$ is zero.