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Physics · 2024 · 3 marks
CBSE 2024 · Region 4 · Set 2 · Q23
A thin spherical conducting shell of radius R has a charge q. A point charge Q is placed at the centre of the shell. Find (i) the charge density on…
A thin spherical conducting shell of radius R has a charge q. A point charge Q is placed at the centre of the shell. Find (i) the charge density on the outer surface of the shell and (ii) the potential at a distance of $\displaystyle (\mathrm{R}/2)$ from the centre of the shell.
Marking-scheme solution
(i)
When a point charge Q is placed at the centre of the shell, a charge $\displaystyle (-Q)$ is induced at its inner surface; consequently the net charge on the outer surface of the shell $\displaystyle =q+Q$.
Charge density on outer surface of the shell:
$\displaystyle \sigma=\frac{\text { charge }}{\text { Area }}$
$\displaystyle =\frac{q+Q}{4 \pi R^{2}}$
(ii)
Potential due to shell at a distance of (R/$\displaystyle 2$) from the centre of the shell:
$\displaystyle V_{1}=\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{R}$
Potential due to charge Q at a distance of (R/$\displaystyle 2$) from the centre of the shell:
$\displaystyle V_{2}=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{Q}{\dfrac{R}{2}}$
Net potential at a distance of (R/$\displaystyle 2$) from the centre of the shell:
$\displaystyle V=V_{1}+V_{2}$
$\displaystyle V=\frac{1}{4 \pi \varepsilon_{0} R}(q+2 Q)$
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CBSE Class 12 Physics past-paper question from the 2024 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.