A circular pan of radius b = 10.10 cm has a plastic bottom and metallic side wall of height h = 2.20 cm . It is filled with solution of resistivity 2.20 ?·m. A metal disk of radius a = 1.10 cm and height h is placed at the center of the pan, as shown in the figure. Assume that the side wall and the disk are perfect conductors.
(a) Assume that a current of 3.70 A is flowing between the metal disk and the metallic side wall. Use a cylindrical coordinate system (r,?,z) with the origin at the bottom center of the central metal disk and the z axis coincident with the axis of the disk; symmetry immediately guarantees that the current density should not depend on the angle ?. Find the current density at a location r = 2.27 cm , z = 1.05 cm .
(b) What is the voltage between the metal disk and the metallic side wall?
(c) What is the resistance of the conducting solution in this geometry?