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JEE Main20231 Feb 2023Morning ShiftPhysicsMagnetic Effects of CurrentActual

Find the magnetic field at the point P in figure. The curved portion is a semicircle connected to two long straight wires.

Options

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

Correct answer

C. μ 0 i 2 r 1 2 + 1 2 π

Step-by-step solution

Magnitude of magnetic field due to semi-infinite portion of wire AB at point C is B 1 = μ 0 i 4 π r Magnitude of magnetic field due to semicircular arc BD at point C is B 2 = μ 0 i 4 r Magnitude of magnetic field due to semi-infinite portion DE at point C is 0. Using right-hand rule, it can be seen that directions of B 1 → and B 2 → are both outwards from the plane. Therefore, the magnitude of net magnetic field at point C is B = B 1 + B 2 = μ 0 i 2 r 1 2 + 1 2 π

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