A charge Q is distributed over three concentric spherical shells of… | JEE Main 2019 (10 Jan, Shift 1)

Q96JEE Main 2019 · 10 JAN · SHIFT 1Medium

Electric Potential & Equipotentials

A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r < a, would be -

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Answer: (d)

Equal $\sigma$ : $q \propto$ radius $^2$ , so $q_a = \frac{Qa^2}{a^2 + b^2 + c^2}$ , etc.
For $r < a$ the potential is the sum of the shell surface potentials: $V = k\left(\frac{q_a}{a} + \frac{q_b}{b} + \frac{q_c}{c}\right)$ .
$V = \frac{Q(a + b + c)}{4\pi\varepsilon_0(a^2 + b^2 + c^2)}$
So the answer is (d).

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