Consider a conductor with mu, epsilon, sigma representing the absolute permeability, permittivity, and conductivity respectively. In a conductor, a plane wave propagates as e^i(beta z - ext) where...

Consider a conductor with mu, epsilon, sigma representing the absolute permeability, permittivity, and conductivity respectively. In a conductor, a plane wave propagates as e^i(beta z - ext) where beta = k_r + ik_i is the complex wave number, (a) Determine beta and the skin depth d (we did this step by step in class, repeat the procedure here). In class we defined a "good conductor" as one where tau 1/omega where tau = epsilon/sigma is time constant that the conductor expels charge. We can re-arrange this expression into the form sigma/epsilon omega 1 Similarly, we would define a "bad conductor" as one where sigma/epsilon omega 1 (b) Show that the skin depth for a bad conductor is d 2/sigma Squareroot epsilon/mu. (c) Show that the skin depth for a good conductor is d lambda/2 pi where A is the wavelength in the conductor given by lambda = 2 pi/k, and. (d) Find the skin depth (in nanometers) for a typical metal with sigma = 2 pi/k, and. (d) Find the skin depth (in nanometers) for a typical metal with sigma = 10^7 (Ohm m)^-1 for green light with a frequency of omega = 3.5 times 10^15 s^-1 where epsilon = epsilon_0 and mu = mu_0. (e) Show that for a good conductor the magnetic field lags the electric field by 45 degree and find the ratio of their amplitudes.