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A wire in the form of a square of side a carries a current i . Then, the magnetic induction at the centre of the square wire is (magnetic permeability of free space = μ 0 ).

Options

  1. Aμ 0 i 2 π a
  2. Bμ 0 i 2 π a
  3. C2 2 μ 0 i π a
  4. Dμ 0 i 2 π a

Correct answer

C. 2 2 μ 0 i π a

Step-by-step solution

Magnetic field due to one side of the square at centre O. B 1 = μ 0 4 π . 2 i sin ⁡ 45 o a 2 ⇒ B 1 = μ 0 4 π . 2 2 i a Hence, magnetic field at centre due to all sides B n e t = 4 B 1 = μ 0 2 2 i π a

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