JEE Main · 2026 · 24 Jan 2026 · Shift 1 · Electrostatics

The potential a shell of charge $q$ and radius $R_s$ produces at a field point of radius $r$ is $\frac{1}{4\pi {\epsilon }_0}\frac{q}{r}$ when $r\ge R_s$ and $\frac{1}{4\pi {\epsilon }_0}\frac{q}{R_s}$ when $r<R_s$. At shell A ($r=a$) the larger shells B and C enclose it, so $V_A=\frac{1}{4\pi {\epsilon }_0}\left(\frac{q_1}{a}+\frac{q_2}{b}+\frac{q_3}{c}\right)$. At shell B ($r=b$), A lies inside and C outside, so $V_B=\frac{1}{4\pi {\epsilon }_0}\left(\frac{q_1+q_2}{b}+\frac{q_3}{c}\right)$. At shell C ($r=c$) all charges lie inside, so $V_C=\frac{1}{4\pi {\epsilon }_0}\left(\frac{q_1+q_2+q_3}{c}\right)$. These are the potentials of A, B and C respectively.