Question

For electromagnetic waves, how do you tell which direction the wave is propagating? And when switching between E and B using E=cB, how do you know which way the other wave is propagating? Using this general format -- > E=Esin(kz-wt) and B=Bsin(kz-wt)

Answer 1

The wave vector indicates the direction of propagation of the wave

So the general argument of sin or cos in the wave equation is

where

Now suppose the wave is propagating in the Z direction. Then the wave vector will have only z component.

and hence

Therefore the wave with is propagating in the z direction.

The cross product electric field vector and magnetic field vector gives the direction of propagation. Hence

So if E is along the x axis and B is along the y axis then, k will be along the z axis

Because

Therefore the wave equation is

where