JEE Main 2026 — Jan 24, Shift 1 — Physics solution

JEE Main2026Jan 24, Shift 1Physics

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 :

A
$\frac{1}{4 π ϵ _{0}} (\frac{q _{1} + q _{2} + q _{3}}{a}), \frac{1}{4 π ϵ _{0}} (\frac{q _{1} + q _{2} + q _{3}}{b}), \frac{1}{4 π ϵ _{0}} (\frac{q _{1} + q _{2} + q _{3}}{c})$
B
$\frac{1}{4 π ϵ _{0}} (\frac{q _{1} + q _{2} + q _{3}}{a}), \frac{1}{4 π ϵ _{0}} (\frac{q _{1} + q _{2}}{b} + \frac{q _{3}}{c}), \frac{1}{4 π ϵ _{0}} (\frac{q _{1}}{a} + \frac{q _{2}}{b} + \frac{q _{3}}{c})$
C
$\frac{1}{4 π ϵ _{0}} (\frac{q _{1}}{a} + \frac{q _{2}}{b} + \frac{q _{3}}{c}), \frac{1}{4 π ϵ _{0}} (\frac{q _{1} + q _{2}}{b} + \frac{q _{3}}{c}), \frac{1}{4 π ϵ _{0}} (\frac{q _{1} + q _{2} + q _{3}}{c})$
D
$\frac{1}{4 π ϵ _{0}} (\frac{q _{1}}{a} + \frac{q _{2}}{b} + \frac{q _{3}}{c}), \frac{1}{4 π ϵ _{0}} (\frac{q _{1} + q _{2} + q _{3}}{b}), \frac{1}{4 π ϵ _{0}} (\frac{q _{1} + q _{2} + q _{3}}{c})$

Solution

Use the result that a uniformly charged spherical shell of charge $Q$ and radius $r$ contributes potential $\frac{k Q}{r}$ at points on or outside it, and $\frac{k Q}{r}$ (constant equal to surface value) at points inside it.

Assume $a < b < c$ with charges $q_{1}, q_{2}, q_{3}$ on shells A, B, C.

At shell A (radius $a$ ): point lies on shell A and inside shells B and C.

$V_{A} = \frac{k q _{1}}{a} + \frac{k q _{2}}{b} + \frac{k q _{3}}{c}$ .

At shell B (radius $b$ ): point lies outside A, on B, inside C.

$V_{B} = \frac{k q _{1}}{b} + \frac{k q _{2}}{b} + \frac{k q _{3}}{c} = \frac{k ( q _{1} + q _{2} )}{b} + \frac{k q _{3}}{c}$ .

At shell C (radius $c$ ): point lies outside A and B, on C.

$V_{C} = \frac{k ( q _{1} + q _{2} + q _{3} )}{c}$ .

Matches option (3).

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