Calculating Ohmic Heating Loss 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.

Homework Equations

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

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($$\sigma$$) ((Ee^(-kz)e^i(kz-$$\omega$$t))^2)/2

is this right? do i need to simplify if I am 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?