(a) In a metal, the electrons can be assumed to be essentially free. Show that the drift v...

(a) In a metal, the electrons can be assumed to be essentially free. Show that the drift velocity of the electron satisfies the following equation

  where ν represents the collision frequency. Calculate the steady state current density (J = – N q v) and show that the conductivity is given by

(b) If r represents the displacement of the electron, show that

which represents the polarization. Using the above equation show that

which represents the dielectric constant variation for a free electron gas.