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 q₁,q₂ and q₃ respectively. The potentials of the spheres A,B and C respectively, are :

Solution

Physics sir · 3 steps

Each shell acts like a point charge outside it and gives a constant potential inside it. Add up all three.

1. One shell alone. A shell of charge q and radius R gives potential 1/4πε₀q/r at a point outside it (r ≥ R). Everywhere inside it, the potential stays at its surface value 1/4πε₀q/R.
2. Superpose. The potential at any shell is the sum of the contributions from all three. Shells inside or on the point use the distance r. Shells outside the point use their own radius.

   Shell	From q₁	From q₂	From q₃
   A (r = a)	q₁/a	q₂/b (inside B)	q₃/c (inside C)
   B (r = b)	q₁/b (outside A)	q₂/b	q₃/c (inside C)
   C (r = c)	q₁/c	q₂/c	q₃/c

3. So. V_A = 1/4πε₀(q₁/a+q₂/b+q₃/c), V_B = 1/4πε₀((q₁+q₂)/b+q₃/c) and V_C = 1/4πε₀(q₁+q₂+q₃)/c. This matches option (d).

The idea to keep. For concentric shells, use the distance for every shell inside or on the point and the shell's own radius for every shell outside it. Then add the three terms.

Answer from the NTA final answer key. Solution by PrepWiser.