Question

A metallic ring of mass m and radius l is falling under gravity in a region having AglaSem Schools a magnetic field. If z is the vertical direction, the z-component of magnetic field is Bz = Bo (1+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,  and acceleration due to gravity g.

Answer 1

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 !!