Question

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.

Answer 1

Magnetic lines of force have a number of important properties, which include: They seek the path of least resistance between opposite magnetic poles. In a single bar magnet as shown to the right, they attempt to form closed loops from pole to pole. They never cross one another.

Answer 2

Hey !!

Rate of change of flux = dΦ / dt = (πl²) B₀λ dz/dt

                                      = IR

   I = (πl²λ) B₀ v/R

Energy lost per second = I² R = (πl²λ)² B₀² v²/R

Rate of change in PE = mg dz/dt = mgv

      mgv = (πl²λ)² B₀² v²/R

= v = mgR / (πl²λ)² B₀²

GOOD LUCK !!