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JEE MainPhysicsMagnetic Effects of Current

A steady current I flows through a wire in the xy -plane consisting of three parts: a semi-infinite straight section parallel to the x -axis coming from x = - to x = 0 at y = R , a quarter-circular arc of radius R centered at the origin from (0, R) to (R, 0) , and another semi-infinite straight section parallel to the y -axis going from y = 0 to y = - at x = R . The magnitude of the net magnetic field at the origin (

Options

  1. A₀ I 8 R (8 + )
  2. B₀ I 8 R (4 + 2 )
  3. C₀ I 8 R (4 + )
  4. D₀ I 8 R

Correct answer

C. ₀ I 8 R (4 + )

Step-by-step solution

The wire consists of three segments, and we calculate the magnetic field contribution of each at the origin (0,0) . Segment 1: The semi-infinite straight wire from x = - to x = 0 at y = R . The perpendicular distance to the origin is R . The magnetic field at the origin is B₁ = ₀ I 4 R . By the right-hand rule, its direction is into the plane of the paper ( - k ). Segment 2: The quarter-circular arc from (0, R) to (R, 0) . The magnetic field at the center of a full circle is ₀ I 2R , so for a quarter circle it is B

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