question_answer 48)

  A metallic ring of mass m and radius  (ring being horizontal) is falling under gravity in a region having a magnetic field. If z is the vertical direction, the z-component of magnetic field is . If R is the resistance of the ring and if the ring falls with a velocity , find the energy lost in the resistance. If the ring has reached a constant velocity, use the conservation of energy to determine in terms of m, B, and acceleration due to gravity g.

Answer:

                  Here, As the metallic ring falls under gravity in this magnetic field, magnetic flux linked with the ring changes. Therefore, an emf is induced in the ring. If  is induced current in the ring at any instant, then induced emf =   where  Energy lost/sec in the form of heat produced in the ring = This comes from rate of change of potential energy of ring = (Note that as  = constant, KE of ring is constant)  or   .