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NEETPhysicsMagnetic Effects of Current

A very long conducting wire carrying a steady current i is bent into a hairpin shape consisting of two parallel semi-infinite straight segments and a semi-circular arc of radius R . The arc lies in the xy -plane, centered at the origin, and spans from (0, R) to (0, -R) through the region x > 0 . The top straight segment lies along y = R and the bottom straight segment lies along y = -R . The current i flows from x =

Options

  1. A₀ e v i 4 R [1 - 2 ] towards the bottom segment
  2. B₀ e v i 4 R [1 + 2 ] towards the top segment
  3. C₀ e v i 4 R [1 - 2 ] towards the top segment
  4. DZero

Correct answer

C. ₀ e v i 4 R [1 - 2 ] towards the top segment

Step-by-step solution

Calculate the net magnetic field B at the origin. The top semi-infinite segment carries current in the -x direction. Using the right-hand rule, its magnetic field at the origin is directed out of the page ( +z direction) with magnitude B_ top = ₀ i 4 R . The bottom semi-infinite segment carries current in the +x direction. Its magnetic field at the origin is also directed out of the page ( +z direction) with magnitude B_ bot = ₀ i 4 R . The semi-circular arc carries current clockwise from (0,R) to (0,-R) . Its magn

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