Preamble

The Drude model is a classical model that - despite several oversimplified assumptions - describes

quite well the dynamics of charge carriers in conductive media. According to this model the finite

conductivity of metals is attributed to the collisions with the atoms that electrons undergo as they

move through a solid, while the effects of electron-electron interactions are neglected. The only

parameter that enters the Drude model is average time between collisions r. We have seen in class

that the average (macroscopically observable) electron velocity obeys the following equation of

motion:

dv(t)

m = F(t)-m-

dt

v(t)

T

(1.1)

Problem 1

a) Solve equation (1.1) with the initial condition v(t=0)=0 and assuming a constant force,

i.e. F(t)=-q E, and obtain the general expression of v(t).

b) From the result of part a) calculate the terminal velocity v(t →∞).

c) From the result of part b) determine the expression of the conductivity assuming that the

electron density is n.