- #1

- 265

- 0

## Homework Statement

Show that the general relationship from Maxwell's equations for the conservation of energy

[itex]

\nabla \cdot \textbf{S} + \frac{\partial u}{\partial t} = 0,

[/itex]

where

[itex]

u = \frac{1}{2} \epsilon _{0} \left| \textbf{E} \right| ^{2} + \frac{1}{2 \mu _{0}} \left| \textbf{B} \right| ^{2},

[/itex]

holds for plane wave solutions to Maxwell's equations.

## Homework Equations

Plane wave solutions:

[itex]

\textbf{E} = E_{0} e^{i(\textbf{k} \cdot \textbf{r} - \omega t)}

[/itex]

[itex]

\textbf{B} = B_{0} e^{i(\textbf{k} \cdot \textbf{r} - \omega t)}

[/itex]

## The Attempt at a Solution

I need a starting point. I can use vector identities to try and derive the answer but I need to know what to start from. I've tried starting from various equations but I can't seem to end up with the conservation law. Any help is appreciated.