A clever physics demonstration involves a conducting aluminum ring of radius R=5.0cm and resistance r=2.0×10−4Ω placed around a vertical solenoid. The solenoid has N=500 turns over a length L=20cm and carries a time-varying current I(t)=I0sin(ωt) where I0=8.0A and ω=2π×60Hz. When the frequency is just right, the ring appears to "levitate" at a fixed height above the solenoid, hovering in the alternating magnetic field.
The ring has mass m=12g and is positioned so that the magnetic field through it is uniform and equal to half the field at the center of the solenoid. For the ring to levitate, the time-averaged upward magnetic force must equal its weight.
(a) Find the peak current Iring induced in the ring.
(b) Calculate the time-averaged upward force on the ring and determine whether it can indeed levitate at the given frequency.