JEE Main 2026 — Physics Electromagnetism

2026mcqmedium

There are three co-centric conducting spherical shells $A, B$ and $C$ of radii $a, b$ and $c$ respectively $(c>b>a)$ and they are charged with charge $q_{1}, q_{2}$ and $q_{3}$ respectively. The potentials of the spheres $A, B$ and $C$ respectively, are :

Official previous-year question

Held on 24 Jan 2026 · Verified 6 Jul 2026.

Options

A
$\frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_{1}+q_{2}+q_{3}}{a}\right), \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_{1}+q_{2}+q_{3}}{b}\right), \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_{1}+q_{2}+q_{3}}{c}\right)$
B
$\frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_{1}}{a}+\frac{q_{2}}{b}+\frac{q_{3}}{c}\right), \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_{1}+q_{2}+q_{3}}{b}\right), \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_{1}+q_{2}+q_{3}}{c}\right)$
C
$\frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_{1}}{a}+\frac{q_{2}}{b}+\frac{q_{3}}{c}\right), \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_{1}+q_{2}}{b}+\frac{q_{3}}{c}\right), \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_{1}+q_{2}+q_{3}}{c}\right)$
D
$\frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_{1}+q_{2}+q_{3}}{a}\right), \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_{1}+q_{2}}{b}+\frac{q_{3}}{c}\right), \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_{1}}{a}+\frac{q_{2}}{b}+\frac{q_{3}}{c}\right)$

Did you get this right?

Solution

The potential at any point due to a charged spherical shell of radius $R$ and charge $Q$ is $V = \frac{1}{4\pi\epsilon_o} \frac{Q}{R}$ for points inside or on the surface ( $r \le R$ ), and $V = \frac{1}{4\pi\epsilon_o} \frac{Q}{r}$ for points outside ( $r > R$ ).

Let $k = \frac{1}{4\pi\epsilon_o}$ . The potentials of the three shells $A, B, C$ with radii $a < b < c$ and charges $q_1, q_2, q_3$ are calculated by superposition.

For shell $A$ ( $r = a$ ):

Shell $A$ is on its own surface, while it is inside shells $B$ and $C$ .

$V_A = k\frac{q_1}{a} + k\frac{q_2}{b} + k\frac{q_3}{c} = \frac{1}{4\pi\epsilon_o} \left( \frac{q_1}{a} + \frac{q_2}{b} + \frac{q_3}{c} \right)$

For shell $B$ ( $r = b$ ):

Shell $B$ is outside shell $A$ , on its own surface, and inside shell $C$ .

$V_B = k\frac{q_1}{b} + k\frac{q_2}{b} + k\frac{q_3}{c} = \frac{1}{4\pi\epsilon_o} \left( \frac{q_1 + q_2}{b} + \frac{q_3}{c} \right)$

For shell $C$ ( $r = c$ ):

Shell $C$ is outside shells $A$ and $B$ , and on its own surface.

$V_C = k\frac{q_1}{c} + k\frac{q_2}{c} + k\frac{q_3}{c} = \frac{1}{4\pi\epsilon_o} \left( \frac{q_1 + q_2 + q_3}{c} \right)$

Comparing these expressions with the given options, option (3) matches correctly.

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Options

$\frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_{1}+q_{2}+q_{3}}{a}\right), \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_{1}+q_{2}+q_{3}}{b}\right), \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_{1}+q_{2}+q_{3}}{c}\right)$

$\frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_{1}}{a}+\frac{q_{2}}{b}+\frac{q_{3}}{c}\right), \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_{1}+q_{2}+q_{3}}{b}\right), \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_{1}+q_{2}+q_{3}}{c}\right)$

$\frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_{1}}{a}+\frac{q_{2}}{b}+\frac{q_{3}}{c}\right), \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_{1}+q_{2}}{b}+\frac{q_{3}}{c}\right), \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_{1}+q_{2}+q_{3}}{c}\right)$

$\frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_{1}+q_{2}+q_{3}}{a}\right), \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_{1}+q_{2}}{b}+\frac{q_{3}}{c}\right), \frac{1}{4 \pi \epsilon_{\mathrm{o}}}\left(\frac{q_{1}}{a}+\frac{q_{2}}{b}+\frac{q_{3}}{c}\right)$

Solution

Let $k = \frac{1}{4\pi\epsilon_o}$ . The potentials of the three shells $A, B, C$ with radii $a < b < c$ and charges $q_1, q_2, q_3$ are calculated by superposition.

For shell $A$ ( $r = a$ ):

Shell $A$ is on its own surface, while it is inside shells $B$ and $C$ .

$V_A = k\frac{q_1}{a} + k\frac{q_2}{b} + k\frac{q_3}{c} = \frac{1}{4\pi\epsilon_o} \left( \frac{q_1}{a} + \frac{q_2}{b} + \frac{q_3}{c} \right)$

For shell $B$ ( $r = b$ ):

Shell $B$ is outside shell $A$ , on its own surface, and inside shell $C$ .

$V_B = k\frac{q_1}{b} + k\frac{q_2}{b} + k\frac{q_3}{c} = \frac{1}{4\pi\epsilon_o} \left( \frac{q_1 + q_2}{b} + \frac{q_3}{c} \right)$

For shell $C$ ( $r = c$ ):

Shell $C$ is outside shells $A$ and $B$ , and on its own surface.

$V_C = k\frac{q_1}{c} + k\frac{q_2}{c} + k\frac{q_3}{c} = \frac{1}{4\pi\epsilon_o} \left( \frac{q_1 + q_2 + q_3}{c} \right)$

Comparing these expressions with the given options, option (3) matches correctly.

JEE Main 2026 — Physics Electromagnetism

Options

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JEE Main 2026 — Physics Electromagnetism

Options

Did you get this right?

Solution

Your note

JEE Main Electromagnetism in other years

More JEE Main Electromagnetism questions

Other Physics topics for JEE Main

Mechanics

Modern Physics

Optics

Thermodynamics

Waves & Oscillations

Keep practicing Electromagnetism