# Looking for a way to describe Electromagnetic Field

1. Apr 24, 2017

### Gersty

As the title suggests, I'm looking for a way to explain/describe the EM field to high school seniors. Mechanical transverse waves are easy. But since EM waves travel in a vacuum and require no medium it's hard to form a picture in the mind of the students. What is actually moving?

2. Apr 25, 2017

### scottdave

You may want to start by talking about static magnets and static electricity, then moving on to oscillating magnetic and electric fields. Here's a site which has an idea of where to start. The site says that it is moving, but it is there for now - https://science.hq.nasa.gov/kids/imagers/ems/waves2.html

3. Apr 25, 2017

### robphy

In a wave, the "disturbance" is what moves.
In the animation on the page suggested by @scottdave ,
that "sine-wave pattern of the electric and magnetic fields at an instant" is what moves forward in the next instant of time.

As an analogy, consider a pulse on a horizontal string ( see https://phet.colorado.edu/en/simulation/wave-on-a-string ).
The disturbance at a point on the string is that piece of the string being displaced from zero in the vertical direction.
That disturbance passes and that piece of string returns to zero height.
The neighboring piece of string then experiences the disturbance.
Let's ignore damping and other dissipative factors.

Now for the electromagnetic field...
At each point in space, there is an electric and magnetic field vector.
In a region where the wave disturbance hasn't reached yet, these vectors are zero (for simplicity).

Now suppose you have this disturbance:
this sine-wave pattern of electric and magnetic fields
at an instant: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/imgel2/emwavec.gif.
In the next instant of time, because of this particular pattern [a plane wave],
Maxwell's Equations move that pattern along the axis...
that is, along the axis,
each point has the electric and magnetic field vectors that its neighbor had at the previous instant.

4. Apr 27, 2017

### hilbert2

Two fields are not necessary for description of an EM wave in vacuum. A single vector potential $\mathbf{A}(x,y,z,t)$ tells everything about the field in a region with no electric charges. The vector potential obeys a wave equation similar to that of mechanical displacement waves. Of course high school students can't do vector calculus, but they can probably get some kind of idea from images like this:

5. Apr 27, 2017

### robphy

Presumably, you are referring to a 4-vector $A^u$ since you need the scalar potential $\phi$ as well. Of course, these potentials are not unique because of gauge freedom... so you will likely have trouble explaining a picture of these potentials (to answer the OP).

6. Apr 27, 2017

### hilbert2

The gauge can be chosen in a way that makes the scalar potential vanish at all points that are far from charge densities.

7. Apr 27, 2017

### Orodruin

Staff Emeritus
The OP is looking for a way to explain EM waves to high school students. Using the vector potential and gauge fixing is not going to help in this.

8. Apr 27, 2017

Staff Emeritus
General relativity...inclined plane...just sayin'.

9. Apr 28, 2017

### hilbert2

I guess it's enough to tell the students that because of EM induction the electric and magnetic fields don't behave independently of each other. Just like the state of motion of a block on an inclined plane can be described with less numbers that the state of a block undergoing projectile motion.

10. Apr 28, 2017

### Orodruin

Staff Emeritus
I don't think this answers the question either. The question many students will have and that the OP is looking for a good answer to is "what is moving in the EM wave?" From our experience with other waves, this is a reasonable question - physicists asked it back in the day and even named the hypothetical medium - "aether". Of course, we now know that aether is not necessary and that most aether theories are excluded.

At this level, I would tell the students that there really is not anything that moves apart from the disturbance in the EM field that propagates in the field. The wave is not a motion in a medium, but a change in the EM fields.