I need to prove conservatino of energy in a conductor of real condictivity [itex]\sigma[/itex]. I need opinion on how to proceed. My best guess was to use Poynting's theorem in differential form, which says that the rate at which work is done per unit time per unit volume on the charges in the metal by the EM wave is given by(adsbygoogle = window.adsbygoogle || []).push({});

[tex]-\frac{\partial u}{\partial t}-\nabla \cdot \vec{S}[/tex]

where u is the E-M energy density and S the Poynting vector. Alright, so since this amount of work is done by unit time by unit volume, it must be that the energy in the wave decreases at the opposite rate! An expression of the decrease in wave energy per unit time per unit volume I found is

[tex]\frac{\partial u}{\partial z} v_{ph}[/tex]

where v_ph is the phase velocity.

We made the computation by plugging E = a damped monochormotic plane wave and B = the associated B field, but the two sides were pretty far from equal. In particular, the phase difference btw E and B was particularly bugging.

By the way, I need to find the solution today (it's 18h30 here) absolutely, so help is eminently needed! Heeeelp!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Conservation of energy (wave in a conductor)

**Physics Forums | Science Articles, Homework Help, Discussion**