- #1

dyn

- 758

- 57

I'm following the "derivation" in some lecture notes which shows that the Electric and Magnetic fields are perpendicular to each other and to the direction of propagation. There are 2 points I don't understand

A solution to the wave equation for E-fields is given as

**E**=

**E**exp i(ωt-kz).

_{0}It then states that if the propagation is along z only then ∂/∂x and ∂/∂y of any property is zero. Why is this so ?

Using Gauss's law this then leads to ∂E

_{z}/∂z = 0 which implies E

_{z}is a constant which is set to zero. But we also have ∂E

_{x}/∂x = 0 and ∂E

_{y}/∂y = 0 so why aren't E

_{x}and E

_{y}equal to a constant which can be set to zero ? I realize this would give no wave.

Thanks