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One of the two identical conducting wires of length L is bent in the form of a circular loop and the other one into a circular coil of N identical turns. If the same current is passed in both, the ratio of the magnetic field at the centre of the loop B L to that at the centre of the coil B C , i.e. B L B C will be

Options

  1. A1 N 2
  2. B1 N
  3. CN
  4. DN 2

Correct answer

A. 1 N 2

Step-by-step solution

For a single loop, radius r 1 = L 2 π B L = μ 0 I 2 r 1 = μ 0 I 2 · L × 2 π ...(1) For a circular coil, radius r 2 = L 2 π N B c = μ 0 · I · N 2 r 2 = μ 0 · I · N 2 · L ⋅ 2 π N ...(2) B L B C = 1 N 2 (from eqns (1) and (2))

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