Understanding Vector in EM Wave

[Drakkith]

Hey all. I don't really understand how the fields of an EM wave have a vector. I think I understand the vector of a static EM field, but I'm having trouble understanding it when it comes to an EM wave.
Could someone help me out a bit? Thanks. (I'm sure it's something simple that I just don't get at the moment. Self teaching is frustrating!)

 

[the_emi_guy]

Check out the animation here:
http://mutuslab.cs.uwindsor.ca/schurko/animations/emwave/emwave.htm

As you are watching the animation notice:
If you freeze time (set T = 100 in animation) than both E and H field vectors are sinusoidal functions of distance from the origin.

If you run time (say T=3) but freeze your position both E and H field vectors are sinusoidal functions of time.

 

[Drakkith]

Is it simply that when the wave passes a charge, that charge will be accelerated in a particular direction depending on the phase of the wave at the time of the interaction? And the opposite direction when the phase is 180 degrees later?

 

[the_emi_guy]

Yes, that's it.

You can also notice looking at the animation that when both E and B vectors have zero magnitude (where they cross x-axis), they both have maximum partial derivative with respect to time, and maximum curl. When they have maximum magnitude (at their peaks) they both have zero partial with respect to time and zero curl. These reflect Maxwell's eqns.

$$\vec{\nabla} \times \vec{E}=-\partial_t \vec{B}$$
$$\vec{\nabla} \times \vec{B}=\mu\epsilon\partial_t \vec{E}$$