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BITSAT2017PhysicsMagnetic Effects of CurrentActual

What is the magnetic field at the centre of arc in the figure below?

Options

  1. Aμ 0 4 π · 2 I r 2 + π
  2. Bμ 0 4 π · 2 I r 2 + π 4
  3. Cμ 0 4 π · I r 2 + π
  4. Dμ 0 4 π · I r 2 + π 4

Correct answer

B. μ 0 4 π · 2 I r 2 + π 4

Step-by-step solution

Distance of straight path from O = r 2 Hence, B = B 1 + B 2 = μ 0 4 π · 2 I r 2 + μ 0 4 π 2 π I r 1 4 = μ 0 4 π · 2 I r 2 + π 4

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