# Rectangular waveguide

## Homework Statement

I have a rectangular, hollow, conductor. Something like this:

The length in z direction should be infinite. The propagation of electromagnetic waves in the conductor are given via the equations:

## Homework Equations

$\Delta \vec{E} = \frac{1}{c^2} \frac{\partial^2 \vec{E}}{\partial t^2}$

$\Delta \vec{B} = \frac{1}{c^2} \frac{\partial^2 \vec{B}}{\partial t^2}$

Question 1: Which boundary conditions follow for the E field? And what does that mean for the B field?

## The Attempt at a Solution

Well. Since there are free charges in the conductor, the tangential component of the E field should be 0 (otherwise the charges would start to move). Which in return means the normal component of the B field must also be 0.

Is there more I could derive from this or is that it? My answer seems a bit too simplistic ...