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NEETPhysicsMagnetic Effects of Current

A long conducting wire carrying a steady current I is bent such that it consists of two mutually perpendicular semi-infinite straight segments connected by a quarter-circular arc of radius R . The straight segments are tangent to the ends of the arc. The magnitude of the net magnetic field at the center of curvature of the quarter-circular arc is:

Options

  1. A₀ I 4R [ 1 2 + 2 ]
  2. B₀ I 4R [ 1 2 - 2 ]
  3. C₀ I 4R [ 1 2 + 4 ]
  4. D₀ I 4R [ 2 + 2 ]

Correct answer

A. ₀ I 4R [ 1 2 + 2 ]

Step-by-step solution

The wire consists of three segments: two semi-infinite straight wires and one quarter-circular arc. The magnetic field at the center of curvature due to the first semi-infinite straight wire is: B₁ = ₀ I 4 R The magnetic field due to the quarter-circular arc is: B₂ = 1 4 ( ₀ I 2R ) = ₀ I 8R The magnetic field due to the second semi-infinite straight wire is: B₃ = ₀ I 4 R By the right-hand thumb rule, the magnetic field contributions from all three segments point in the same direction. The net magnetic field magnitu

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