A wire loop with radius b in the x-y plane carries a time-harmonic current I₀ cos ωt.
(a) Find the value of I0 needed to levitate a small sphere with mass m, radius a, and conductivity σ at a height z above the center of the loop. Assume that a << b and that δ << a, where δ is the skin depth of the sphere.
(b) Compare the time-averaged levitation force you calculate with the qualitative estimate made in the text. Comment if they do not agree.