There are three co-centric conducting spherical shells A , B and C of radii a , b and c respectively. The potential of the spheres A , B and C respectively, are :

frac 1 4 π ε 0 (frac q 1 a +frac q 2 b +frac q 3 c ), frac 1 4 π ε 0 (frac q 1 + q 2 b +frac q 3 c ), frac 1 4 π ε 0 (frac q 1 + q 2 + q 3 c )

frac 1 4 π ε 0 (frac q 1 + q 2 + q 3 a ), frac 1 4 π ε 0 (frac q 1 + q 2 + q 3 b ), frac 1 4 π ε 0 (frac q 1 + q 2 + q 3 c )

frac 1 4 π ε 0 (frac q 1 + q 2 + q 3 a ), frac 1 4 π ε 0 (frac q 1 + q 2 b +frac q 3 c ), frac 1 4 π ε 0 (frac q 1 a +frac q 2 b +frac q 3 c )

frac 1 4 π ε 0 (frac q 1 a +frac q 2 b +frac q 3 c ), frac 1 4 π ε 0 (frac q 1 + q 2 + q 3 b ), frac 1 4 π ε 0 (frac q 1 + q 2 + q 3 c )

Physics · Electrostatics

JEE Main 2026 — 24 January, Morning Shift — Question 42

There are three co-centric conducting spherical shells $\mathrm{A}, \mathrm{B}$ and C of radii $\mathrm{a}, \mathrm{b}$ and c respectively. The potential of the spheres $\mathrm{A}, \mathrm{B}$ and C respectively, are :

Option A:
$\frac{1}{4 \pi \epsilon_{0}}\left(\frac{\mathrm{q}_{1}+\mathrm{q}_{2}+\mathrm{q}_{3}}{\mathrm{a}}\right), \frac{1}{4 \pi \epsilon_{0}}\left(\frac{\mathrm{q}_{1}+\mathrm{q}_{2}+\mathrm{q}_{3}}{\mathrm{~b}}\right), \frac{1}{4 \pi \epsilon_{0}}\left(\frac{\mathrm{q}_{1}+\mathrm{q}_{2}+\mathrm{q}_{3}}{\mathrm{c}}\right)$
Option B:
$\frac{1}{4 \pi \epsilon_{0}}\left(\frac{\mathrm{q}_{1}+\mathrm{q}_{2}+\mathrm{q}_{3}}{\mathrm{a}}\right), \frac{1}{4 \pi \epsilon_{0}}\left(\frac{\mathrm{q}_{1}+\mathrm{q}_{2}}{\mathrm{~b}}+\frac{\mathrm{q}_{3}}{\mathrm{c}}\right), \frac{1}{4 \pi \epsilon_{0}}\left(\frac{\mathrm{q}_{1}}{\mathrm{a}}+\frac{\mathrm{q}_{2}}{\mathrm{~b}}+\frac{\mathrm{q}_{3}}{\mathrm{c}}\right)$
Option C:
$\frac{1}{4 \pi \epsilon_{0}}\left(\frac{\mathrm{q}_{1}}{\mathrm{a}}+\frac{\mathrm{q}_{2}}{\mathrm{~b}}+\frac{\mathrm{q}_{3}}{\mathrm{c}}\right), \frac{1}{4 \pi \epsilon_{0}}\left(\frac{\mathrm{q}_{1}+\mathrm{q}_{2}}{\mathrm{~b}}+\frac{\mathrm{q}_{3}}{\mathrm{c}}\right), \frac{1}{4 \pi \epsilon_{0}}\left(\frac{\mathrm{q}_{1}+\mathrm{q}_{2}+\mathrm{q}_{3}}{\mathrm{c}}\right)$
Correct
Option D:
$\frac{1}{4 \pi \epsilon_{0}}\left(\frac{\mathrm{q}_{1}}{\mathrm{a}}+\frac{\mathrm{q}_{2}}{\mathrm{~b}}+\frac{\mathrm{q}_{3}}{\mathrm{c}}\right), \frac{1}{4 \pi \epsilon_{0}}\left(\frac{\mathrm{q}_{1}+\mathrm{q}_{2}+\mathrm{q}_{3}}{\mathrm{~b}}\right), \frac{1}{4 \pi \epsilon_{0}}\left(\frac{\mathrm{q}_{1}+\mathrm{q}_{2}+\mathrm{q}_{3}}{\mathrm{c}}\right)$

Answer: C

Step-by-step solution

\begin{aligned} & \mathrm{V}_{\mathrm{A}}=\frac{\mathrm{Kq}_{1}}{\mathrm{a}}+\frac{\mathrm{Kq}_{2}}{\mathrm{~b}}+\frac{\mathrm{Kq}_{3}}{\mathrm{c}}=\frac{1}{4 \pi \varepsilon_{0}}\left(\frac{\mathrm{q}_{1}}{\mathrm{a}}+\frac{\mathrm{q}_{2}}{\mathrm{~b}}+\frac{\mathrm{q}_{3}}{\mathrm{c}}\right) & \mathrm{V}_{\mathrm{B}}=\frac{\mathrm{Kq}_{1}}{\mathrm{~b}}+\frac{\mathrm{Kq}_{2}}{\mathrm{~b}}+\frac{\mathrm{Kq}_{3}}{\mathrm{c}}=\frac{1}{4 \pi \varepsilon_{0}}\left(\frac{\mathrm{q}_{1}+\mathrm{q}_{2}}{\mathrm{~b}}+\frac{\mathrm{q}_{3}}{\mathrm{c}}\right) & \mathrm{V}_{\mathrm{C}}=\frac{\mathrm{Kq}_{1}}{\mathrm{c}}+\frac{\mathrm{Kq}_{2}}{\mathrm{c}}+\frac{\mathrm{Kq}_{3}}{\mathrm{c}}=\frac{1}{4 \pi \varepsilon_{0}}\left(\frac{\mathrm{q}_{1}+\mathrm{q}_{2}+\mathrm{q}_{3}}{\mathrm{c}}\right) \end{aligned}

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Exam: JEE Main 2026
Paper: 24 January, Morning Shift
Subject: Physics
Chapter: Electrostatics
Topic: Properties of Conductors and Redistribution of Charge

Answer: C

Step-by-step solution

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