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A conducting wire ab of length l , resistance r and mass m starts sliding down at t = 0 down a smooth vertical, thick pair of perfectly conducting rails as shown in the figure. A uniform magnetic field B exist in the space in a direction perpendicular to the plane of the rails. What will be the final constant speed of wire?

Options

  1. Am g r B 2 l 2
  2. Bm g r 2 B 2 l 2
  3. Cm g r 2 B l 2
  4. Dm g r B l 2

Correct answer

A. m g r B 2 l 2

Step-by-step solution

If there are no dissipating forces then the system will oscillate but if there is some small resistance then the acceleration of the conductor is related to the net force as m d v d t = m g - i l B = m g - B 2 l 2 v r When the rod attains the steady constant speed, d v d t is zero. Hence v 0 = m g r B 2 l 2

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