Concentric metallic hollow spheres of radii R and 4R hold charges Q1… | JEE Main 2020 (3 Sep, Shift 2)

Q90JEE Main 2020 · 3 SEP · SHIFT 2Medium

Electric Potential & Equipotentials

Concentric metallic hollow spheres of radii R and 4R hold charges Q1 and Q2 respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference V(R) – V(4R) is:

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Answer: (c)

Equal $\sigma$ : $\frac{Q_1}{R^2} = \frac{Q_2}{16R^2} \Rightarrow Q_2 = 16Q_1$ (not needed further).
The outer shell adds the same potential at $R$ and $4R$ , so only $Q_1$ matters.
$V(R) - V(4R) = \frac{Q_1}{4\pi\varepsilon_0}\left(\frac{1}{R} - \frac{1}{4R}\right) = \frac{3Q_1}{16\pi\varepsilon_0 R}$
So the answer is (c).

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