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JEE Main20262 April 2026Morning ShiftPhysicsMagnetic Effects of CurrentActual

Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centres P and Q of a semicircular arc are B₁ and B₂ respectively, then the ratio B₁ B₂ is _______.

Options

  1. A2 + 1 +
  2. B1 + 1 -
  3. C2 + 1 -
  4. D1 + 2 -

Correct answer

A. 2 + 1 +

Step-by-step solution

For the first figure, the magnetic field at the centre P is the vector sum of the magnetic fields due to two semi-infinite straight wires and one semicircular arc. The magnetic field due to the top semi-infinite wire at P is B_ 1a = ₀ I 4 r directed into the plane. The magnetic field due to the bottom semi-infinite wire at P is B_ 1b = ₀ I 4 r directed into the plane. The magnetic field due to the semicircular arc at P is B_ 1c = ₀ I 4r = ₀ I 4 r directed into the plane. The total magnetic field at P is B₁ = B_ 1a

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