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Consider a toroid of circular cross-section of radius b , major radius R much greater than minor radius b , (see diagram) find the total energy stored in magnetic field of toroid -

Options

  1. AB 2 π 2 b 2 R 2 μ 0
  2. BB 2 π 2 b 2 R 4 μ 0
  3. CB 2 π 2 b 2 R 8 μ 0
  4. DB 2 π 2 b 2 R μ 0

Correct answer

D. B 2 π 2 b 2 R μ 0

Step-by-step solution

B = μ 0 N i 2 R ϕ = π b 2 × B × N ϕ = L i L = ϕ i = μ 0 N 2 b 2 2 R , with   b < < < R E = 1 2 L i 2 = μ 0 N 2 i 2 4 R b 2

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