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JEE MainPhysicsMagnetic Effects of Current

A wire carrying a steady current I is bent into a U-shape in the xy -plane. It consists of two semi-infinite straight sections, y=R and y=-R for x 0 , connected by a semicircular arc of radius R centred at the origin. An infinitely long straight wire, also carrying current I , is placed in the xy -plane parallel to the x -axis. If the net magnetic field at the origin is zero, the distance of the infinitely long strai

Options

  1. A2R 2 +
  2. B2R 4 +
  3. C2R
  4. DR 2 +

Correct answer

A. 2R 2 +

Step-by-step solution

The magnetic field at the origin due to the U-shaped wire is the sum of the fields from the two semi-infinite straight sections and the semicircular arc. The magnetic field due to each semi-infinite straight section at the origin is B_ straight = ₀ I 4 R . Since there are two such sections and their fields point in the same direction, their combined contribution is 2 ₀ I 4 R = ₀ I 2 R . The magnetic field due to the semicircular arc at the origin is B_ arc = ₀ I 4R = ₀ I 4 R . By the right-hand rule, all these cont

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