1. The problem statement, all variables and given/known data The problem I have is that we are asked to show the complex relative permittivity of a good conductor is erc = 1 + i(sigma)/(omega*epsilon_0) where sigma is the conductivity and omega is the frequency of an electromagnetic wave in the medium. This is fine, I calculated it, the equation is given, it must be right. Now, we are also told that sigma is much greater than omega*epsilon_0, so the approximation it invites us to make is that erc = i(sigma)/(omega*epsilon_0). I think this is probably right so far. The problem comes now. I am asked to find the energy density of the E-field in the wave. This is given by u = (1/2)E.D. Of course, this uses real values. I think Dc = erc*epsilon_0*Ec, and then I just take the real part of Dc to get D. However, the complex relative permittivity (assumed totally imaginary in our approximation) introduces a pi/2 phase shift, turning what was, say, a cosine in the E-field to a sine in the D-field. When I do (1/2)E.D, this results in something of the form sin(x)cos(x) (x being wave stuff) which boils down to something of the form sin(2x), which can of course be negative. Is all of this allowed? What has gone wrong if it isn't?