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A thin flexible wire of length L is connected to a battery (negligible in size as compared to the wire) to form a closed loop. The battery drives a current I in the wire. When the system is put in a uniform magnetic field of strength B perpendicular to the plane in which the wire is placed, the wire takes the shape of a circle. The tension in the wire is

Options

  1. AI B L
  2. BI B L π
  3. CI B L 2 π
  4. DI B L 4 π

Correct answer

C. I B L 2 π

Step-by-step solution

L = 2 π R R = L 2 π 2 T sin d θ = F m For small angles, sin ( d θ ) ≈ d θ 2 T d θ = I d L B sin 90 ° = I R . d θ . B T = I R B = I L B 2 π

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