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NTA Abhyas JEE Main2020PhysicsMagnetic Effects of CurrentPractice

A current-carrying wire is placed in the grooves of an insulating semicircular disc of radius R , as shown. The current enters at point A and leaves from the point B . Determine the magnetic field at point D .

Options

  1. Aμ 0 I 8 π R 3
  2. Bμ 0 I 4 π R 3
  3. C3 μ 0 I 4 π R
  4. Dnone of these

Correct answer

B. μ 0 I 4 π R 3

Step-by-step solution

The angle formed by lines from each end of diameter to any point of the semicircle is 90 ° . Therefore, CB   ⊥ DB and CA ⊥ DA . Magnetic field due to wire AC , B AC = μ 0 I 4 π 2 R sin 30 ° cos 30 ° - cos 90 ° = 3 μ 0 I 8 π R Magnetic field due to wire BC , B BC = μ 0 I 4 π 2 R sin 60 ° cos 60 ° - cos 90 ° = μ 0 I 8 3 π R = 3 μ 0 I 24 π R B → net = B A - B B = 3 μ 0 I 8 π R 1 - 1 3 = 2 3 μ 0 I

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