A solenoid coil with N turns per unit length, a length of L, and a radius of r₀ is used to image an object of radius r0 with uniform resistivity of ρ. The coil is excited with a current I(t) = cos(2πν₀t).

(a) What is the average power dissipated in the object? What is the voltage induced for a cylindrical shell of radius r?

(b) Given that the differential conductance of a cylindrical shell with length L, radius r, and resistivity ρ is dG = Ldr/(2πrρ), show that the effective electrical resistance of a solenoid is given by (13.79).