Question

Consider an initially neutral hollow conducting spherical shell with inner radius $r$ and outer radius $2 r$. A point charge $+Q$ is now placed inside the shell at a distance $r / 2$ from the centre. The shell is then grounded by connecting the outer surface to the earth. $P$ is an external point at a distance $2 r$ from the point charge $+Q$ on the line passing through the centre and the point charge $+Q$ as shown in the figure.

The magnitude of the force on a test charge $+q$ placed at $P$ will be

• A. $\frac{1}{4 \pi e_{0}} \frac{q Q}{4 r^{2}}$
• B. $\frac{1}{4 \pi \varepsilon_{0}} \frac{9 q Q}{100 r^{2}}$
• C. $\frac{1}{4 \pi \varepsilon_{0}} \frac{4 q Q}{25 r^{2}}$
• D. 0

Answer 1

Answer: (D)

When a charge $+Q$ is placed inside the shell, it induces a charge $-Q$ on the inner surface of shell and a charge of $+Q$ appears on outer surface of shell.

When outer surface is earthed, charge on outer surface is neutralised.

As, now net charge inside the shell is zero.
Hence, net field outside the shell is zero.
$\therefore $ Force on charge at an external point $P$ is zero.