The region between two concentric conducting spheres with radii a and b is filled with a conducting material with resistivity rho. (a) Show that the resistance between the spheres is given by R=rho4π (1a−1b) (b) Derive an expression for the current density as a function of radius, in terms of the potential difference Vab between the spheres. (c) Show that the result in part (a) reduces to Eq. (25.10) when the separation L=b−a between the spheres is small.

Suppose that two tanks, 1 and 2, each with a large opening at the top, contain different liquids. a small hole is made in the side of each tank at the same depth 1.57 m below the liquid surface, but the hole in tank 2 has 2.49 times the cross-sectional area of the hole in tank 1. (a) what is the ratio ρ1/ρ2 of the densities of the liquids if the mass flow rate is the same for the two holes? (b) what is the ratio rv1/rv2 of the volume flow rates from the two tanks? (c) at one instant, the liquid in tank 1 is 14.9 cm above the hole. if the tanks are to have equal volume flow rates, what height above the hole must the liquid in tank 2 be just then?