JEE PYQ: Electrostatics Question 54
Question 54 - 2019 (10 Jan Shift 1)
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:
(1) $\frac{Q}{12\pi\varepsilon_0}\frac{ab + bc + ca}{abc}$
(2) $\frac{Q(a^2 + b^2 + c^2)}{4\pi\varepsilon_0(a^3 + b^3 + c^3)}$
(3) $\frac{Q}{4\pi\varepsilon_0(a + b + c)}$
(4) $\frac{Q(a + b + c)}{4\pi\varepsilon_0(a^2 + b^2 + c^2)}$
Show Answer
Answer: (4)
Solution
Equal surface charge densities: $\sigma_a = \sigma_b = \sigma_c$. So $Q_a : Q_b : Q_c = a^2 : b^2 : c^2$. $V = \frac{KQ_a}{a} + \frac{KQ_b}{b} + \frac{KQ_c}{c} = K\sigma \cdot 4\pi(a + b + c) = \frac{Q(a+b+c)}{4\pi\varepsilon_0(a^2+b^2+c^2)}$.
BETA
