## ohmic heating in a conductor

question
For a plane wave of the form E(z,t)=Ee^i(kz-wt) and B(z,t)=Ee^(-kz)*e^i(kz-wt) write down the time-averaged ohmic heating loss per unit volume for any z.

2. Relevant equations
J=$$\sigma$$E
Maxwell's equations for linear media

3. The attempt at a solution
not sure where to start, i need a nudge
 You know E, and you gave us the equation for J, so you know J. Do you know how to find the Ohmic heating, given J and E?
 yea i figured it out. you take the dot product of J and E.

## ohmic heating in a conductor

ok now i have Re($$\sigma$$) ((Ee^(-kz)e^i(kz-$$\omega$$t))^2)/2

is this right? do i need to simplify if im going to integrate with respect to z?
 Careful with the Re(). Remember Re(A) Re(B) is not equal to Re(AB) since there are cross terms. Here it looks like you assumed Re(E^2) = (Re(E))^2, which it's not.
 so is what i have already wrong?

 Tags electrodynamics, ohmic, plane wave