ohmic heating in a conductor

smcdan32

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=[tex]\sigma[/tex]E
Maxwell's equations for linear media


3. The attempt at a solution
not sure where to start, i need a nudge

phyzguy

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?

smcdan32

yea i figured it out. you take the dot product of J and E.

smcdan32

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

is this right? do i need to simplify if im going to integrate with respect to z?

phyzguy

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.

smcdan32

so is what i have already wrong?