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.

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

 

[sardar]

Hi there, I can definitely help clarify the concept of vector in an EM wave for you. First, let's define what we mean by vector in this context. A vector is a quantity that has both magnitude and direction. In the case of an EM wave, the vector refers to the direction of the electric and magnetic fields that make up the wave.

In an EM wave, the electric and magnetic fields are perpendicular to each other and to the direction of propagation of the wave. This means that they form a three-dimensional vector, with one component in the direction of the electric field, one in the direction of the magnetic field, and one in the direction of propagation.

The magnitude of these fields determines the strength of the wave, while the direction of the vector determines the polarization of the wave. This polarization can be linear, circular, or elliptical, depending on the orientation of the electric and magnetic fields.

It's important to remember that the vector of an EM wave is constantly changing as the wave propagates. This is because the electric and magnetic fields are oscillating, meaning they are constantly changing in magnitude and direction. This oscillation is what allows the wave to carry energy and information through space.

I hope this helps clear up any confusion you may have had about the vector in an EM wave. Keep up the self-teaching, it can be frustrating at times but it's also very rewarding!