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JEE Main20204 Sep 2020Morning ShiftPhysicsMagnetic Effects of CurrentActual

A wire A , bent in the shape of an arc of a circle, carrying a current of 2 A and having radius 2 cm and another wire B , also bent in the shape of an arc of a circle, carrying a current of 3 A and having radius of 4 cm , are placed as shown in the figure. The ratio of the magnetic fields due to the wires A and B at the common centre O is:

Options

  1. A4 : 6
  2. B6 : 4
  3. C2 : 5
  4. D6 : 5

Correct answer

D. 6 : 5

Step-by-step solution

Given, Current in the arc A is i 1 = 2   A Current in the arc B is i 2 =   3   A Radius of arc A is R 1 = 2   cm Radius of arc B is R 2 = 4   cm Magnetic field at the centre of circular current carrying arc is given by B C = μ 0 i 4 π R θ     . . . ( 1 ) Where, θ is the angle subtended at centre. Magnetic field at the centre due to arc A and B is given by B A = μ 0 i 1 4 πR 1 2 π - π 2     . . . 2 B B = μ 0 i 2 4 πR 2 2 &

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