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A very long solenoid is made out of a wire with n turns per unit length. The radius of the cylinder is a and is negligible compared to its length l . The interior of the cylinder is filled with materials such that the linear magnetic permeability varies with the distance r from axis according to μ r = μ 1 = c o n s t a n t ; f o r 0 < r < b μ 2 = c o n s t a n t ; f o r b < r < a The self-inductance of the solenoid i

Options

  1. Aπ n 2 l μ 1 b 2 + μ 2 b 2
  2. Bπ n 2 l μ 1 + μ 2 a 2
  3. Cπ n 2 l μ 1 b 2 + μ 2 a 2 - b 2
  4. Dπ n 2 l μ 1 b 2 + μ 1 + μ 2 a 2

Correct answer

C. π n 2 l μ 1 b 2 + μ 2 a 2 - b 2

Step-by-step solution

Self-inductance of the solenoid is given by L = μ r n 2 π a 2 l Here, μ varies with distance r . So, the self-inductance can be written as L = μ 1 n 2 l π b 2 0 < r < b + μ 2 n 2 l π a 2 - π b 2 b < r < a = π n 2 l μ 1 b 2 + μ 2 a 2 - b 2

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