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Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectromagnetic Induction

A rectangular wire-frame of width d , mass m , and resistance R has a large length. As shown in the figure, a uniform magnetic field B is present to the left of the frame. At t = 0 , a constant force F begins pushing the frame into the magnetic field region. Determine the acceleration of the frame once its speed reaches v .

Options

  1. ARF - v d B mR
  2. BRF + v d^2 B^2 mR
  3. CF - v d^2 B^2 m
  4. DRF - v d^2 B^2 mR

Correct answer

D. RF - v d^2 B^2 mR

Step-by-step solution

When the rectangular wire-frame enters the magnetic field with velocity v , an induced motional emf is generated in its leading edge of length d . The induced emf is given by: = Bvd The induced current in the frame is: I = R = Bvd R This current flowing through the leading edge experiences a magnetic force opposing the motion of the frame (according to Lenz's law). The magnitude of this magnetic force is: F_m = IdB = ( Bvd R )dB = B^2 d^2 v R The net force acting on the frame is the applied force F minus the opposi

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