JEE Main 2026 — Electrostatics Question with Solution

The potential at any point due to a charged spherical shell of radius $R$ and charge $Q$ is $V=\frac{1}{4\pi {ϵ}_o}\frac{Q}{R}$ for points inside or on the surface ($r\le R$), and $V=\frac{1}{4\pi {ϵ}_o}\frac{Q}{r}$ for points outside ($r>R$).
Let $k=\frac{1}{4\pi {ϵ}_o}$. 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 $C$.
$V_A=k\frac{q_1}{a}+k\frac{q_2}{b}+k\frac{q_3}{c}=\frac{1}{4\pi {ϵ}_o}\left(\frac{q_1}{a}+\frac{q_2}{b}+\frac{q_3}{c}\right)$
For shell $B$ ($r=b$):
Shell $B$ is outside shell $A$, on its own surface, and inside shell $C$.
$V_B=k\frac{q_1}{b}+k\frac{q_2}{b}+k\frac{q_3}{c}=\frac{1}{4\pi {ϵ}_o}\left(\frac{q_1+q_2}{b}+\frac{q_3}{c}\right)$
For shell $C$ ($r=c$):
Shell $C$ is outside shells $A$ and $B$, and on its own surface.
$V_C=k\frac{q_1}{c}+k\frac{q_2}{c}+k\frac{q_3}{c}=\frac{1}{4\pi {ϵ}_o}\left(\frac{q_1+q_2+q_3}{c}\right)$
Comparing these expressions with the given options, option (3) matches correctly.