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Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectromagnetic Induction

As shown in the figure, a long U-shaped wire of width l is positioned in a perpendicular magnetic field B . A wire of length l slides on the U-shaped wire towards the right at a constant velocity v . The resistance of all the wires is r per unit length. At t = 0 , the sliding wire is situated close to the left edge of the U-shaped wire. Determine the force needed to maintain the sliding wire's constant velocity v at

Options

  1. AB^2 l^2 v 2r(2l + vt)
  2. BB^2 l^2 v r(2l + vt)
  3. CB^2 l^2 v 2r(l + vt)
  4. DB^2 l^2 v r(l + vt)

Correct answer

C. B^2 l^2 v 2r(l + vt)

Step-by-step solution

At time t , the distance moved by the sliding wire towards the right is x = vt . The conducting loop consists of the left edge of the U-shaped wire, the top and bottom segments of the U-shaped wire up to the sliding wire, and the sliding wire itself. The total length of the wire forming the loop is: L = l (left edge) + vt (top segment) + vt (bottom segment) + l (sliding wire) L = 2l + 2vt = 2(l + vt) Since the resistance of all wires is r per unit length, the total resistance of the loop at time t is: R = rL = 2r(l

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