There are three concentric conducting spherical shells A, B and C of radii a, b and c respectively ( c > b > a) and they are charged with charge q₁, q₂ and q₃ respectively. The potentials of the spheres A, B and C respectively, are: (a) (1)/(4πε₀)(q₁/a+q₂/b+q₃/c), (1)/(4πε₀)((q₁+q₂+q₃)/(b)), (1)/(4πε₀)((q₁+q₂+q₃)/(c)) (b) (1)/(4πε₀)((q₁+q₂+q₃)/(a)), (1)/(4πε₀)((q₁+q₂+q₃)/(b)), (1)/(4πε₀)((q₁+q₂+q₃)/(c)) (c) (1)/(4πε₀)((q₁+q₂+q₃)/(a)), (1)/(4πε₀)((q₁+q₂)/(b)+q₃/c), (1)/(4πε₀)(q₁/a+q₂/b+q₃/c) (d) (1)/(4πε₀)(q₁/a+q₂/b+q₃/c), (1)/(4πε₀)((q₁+q₂)/(b)+q₃/c), (1)/(4πε₀)((q₁+q₂+q₃)/(c))

Answer: (d). A shell gives kq/r outside it and kqRshell inside it. VA = k(q₁/a + q₂/b + q₃/c) (A is inside B and C). VB = k((q₁ + q₂)/(b) + q₃/c), VC = k (q₁ + q₂ + q₃)/(c) So the answer is (d).

There are three concentric conducting spherical shells A, B and C of… | JEE Main 2026 (24 Jan, Shift 1)

Q22JEE Main 2026 · 24 JAN · SHIFT 1Difficult

Electric Potential & Equipotentials

There are three concentric 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:

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Answer: (d)

A shell gives $\frac{kq}{r}$ outside it and $\frac{kq}{R_{shell}}$ inside it.
$V_A = k\left(\frac{q_1}{a} + \frac{q_2}{b} + \frac{q_3}{c}\right)$ (A is inside B and C).
$V_B = k\left(\frac{q_1 + q_2}{b} + \frac{q_3}{c}\right)$ , $V_C = k\,\frac{q_1 + q_2 + q_3}{c}$
So the answer is (d).

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