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Current is flowing in conducting wire shaped as shown in the figure. The radius of the curved part is R and the length of straight portion is very large. The value of the magnetic field at the centre O is B = μ 0 I π R k π + 1 4 , where the value of k is

Options

  1. A3 2
  2. B3 8
  3. C9 2
  4. D9 8

Correct answer

B. 3 8

Step-by-step solution

B A = 0 B B = μ 0 4 π 2 π - π / 2 I R B C = μ 0 I 4 π R ∴ B 0 = B A + B B + B C = μ o I 4 π R 3 π 2 + 1 B = μ o I π R 3 8 π + 1 4 B = μ o I π R κ π + 1 4 When κ = 3 8

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