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A rectangular loop of metallic wire is of length a and breadth b and carries a current i . The magnetic field at the centre of the loop is -

Options

  1. Aμ 0   i 4 π   8 a 2 + b 2 a b
  2. Bμ 0   i 4 π 4 a 2 + b 2 a b
  3. Cμ 0   i 4 π 2 a 2 + b 2 a b
  4. Dμ 0   i 4 π a 2 + b 2 a b

Correct answer

A. μ 0   i 4 π   8 a 2 + b 2 a b

Step-by-step solution

B A B = B C D = μ 0 i 4 π   b / 2   sin ⁡ ϕ 1 + sin ⁡ ϕ 1 = μ 0   4 π   .   4 i b   a a 2 + b 2 B B C = B D A = μ 0 4 π   . 4   i a   . b a 2 + b 2 ∴   B = B AB + B B C + B C D + B D A = μ 0 4 π   . 4   i a 2 + b 2   a b + b a + a b + b a = μ 0 4 π   .   8   i a 2 + b 2 a b

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