(a) For a conduction electron in a metal under the influence of an applied electric field, E, show that the ratio of the Fermi velocity, UF, to its drift velocity, vd, is proportional to Ep/E, where Er is the Fermi Energy. (b) Calculate the magnitude of this ratio for a wire with a free electron density, n, of 1029 m3 and the electric field produced by a 3V battery across a 50 cm length of wire. Assume that the mean free path, A, of the electrons is 3 Å.