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Three concentric metal shells A , B and C of respective radii a , b and c ( a < b < c ) have surface charge densities + σ , - σ and + σ respectively. The potential of shell B is:

Options

  1. Aσ ε 0 b 2 - c 2 c + a
  2. Bσ ε 0 a 2 - b 2 a + c
  3. Cσ ε 0 a 2 - b 2 b + c
  4. Dσ ε 0 b 2 - c 2 b + a

Correct answer

C. σ ε 0 a 2 - b 2 b + c

Step-by-step solution

Net potential at B is due to the superposition of potential due to all shells, ∨ B = ∨ B I + ∨ B I I + ∨ B I I I = K 4 π a 2 σ b + K 4 π b 2 - σ b + K 4 π c 2 σ c Required potential of b = σ a 2 ε 0 b - σ b 2 ε 0 b + σ c 2 ε 0 c = σ ε 0 a 2 - b 2 b + c

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