Answer Happy

Problem B3*: A coaxial cable consists of a very long cylindrical wire of radius a surrounded concentrically by a very long cylindrical shell of inside radius b and outside radius c (a < b < c). The inside wire carries a current I along its length, uniformly distributed across its cross section. The outside shell carries a return current of the same magnitude in the opposite direction, also uniformly distributed across its cross section. a) Use Ampere's law to determine the magnetic field at arbitrary points in the three regions p <a, a < p < b, and b< p <c, where p is the radial distance to the point from the common axis of the cylinders. b) Calculate the magnetic energy per unit length of the cable and then use this to determine the inductance of the cable per unit length. c) Assuming that Ohm's law is obeyed in both the inside wire and outer shell and that both conductors have the same electrical conductivity o, determine the Poynting vector at an arbitrary point inside each conductor. d) Show that the power per unit axial length that flows radially into the two conduc- tors is equal to the power per unit length that is dissipated by the electrical resistance of the cable.