# A metallic ring of mass m and radius l (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 v, find the energy lost in the resistance. If the ring has reached a constant velocity, use the conservation of energy to determine v in terms of m, B,  and acceleration due to gravity g.

Here a relation is established between the current induced, velocity of free falling ring and power lost. Let the mass of ring be m and radius l;

Applying Faraday's law of EMI, we have emf induced given by

rate of change of flux. Also, by Ohm's law

We have

Energy lost/second =

Rate of change of

[ as kinetic energy is constant for v=constant]

According to the law of conservation of energy

Thus,

or

This is the required expression of velocity.

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