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 Bz = Bo
(1+λ z). 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, λ and acceleration due to gravity g.
Rate of change of magnetic flux:
Energy lost per second:
Rate of change in PE:
Rate of change =
= mgv
Equate rate of change in PE to energy lost per second:
Energy lost per second:
Rate of change in PE:
Rate of change =
= mgv
Equate rate of change in PE to energy lost per second: