# Visualizing Electromagnetic Waves in 3D Space

I did one module of physics for my GCSE one year ago which taught me about transverse EM waves & the EM spectrum, but since then, I do not understand how a wave would move in 3D space. Can someone show me some animation or something? I can understand it in 2D space (ie on a graph) but not 3D. I also read somewhere that they do not oscilate in space, but in electromagnetic field strength and direction? Is this true?

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I'm not sure what to make of this question, to be honest. What do others think? –  Noldorin Jan 19 '11 at 18:33
Is this a bad question? If so, why? –  Ell Jan 19 '11 at 18:47
I'm relatively new around here, but I'm in favor of allowing this sort of question for what it's worth. –  Ted Bunn Jan 19 '11 at 20:33
I think I've given an answer to something similar recently. Take a look if you want: physics.stackexchange.com/questions/2739/… –  Marek Jan 20 '11 at 9:44
There are people, who lack th ability of making some 3D out of plane sketches in brain. For those such a animation (ideally anaglyphic) would help. –  Georg Jan 20 '11 at 10:40
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Ell, I sympathise. You look at the graphs showing an oscillating electromagnetic wave and misread the transverse axes as spatial. So you think an electromagnetic wave is like the wave you can flick along a skipping rope. No it isn't.

The best way to think about it is that at each point in space where the wave is, there are two little arrows at right angles to each other and to the direction of motion of the wave. One arrow is the electric field, the other is the magnetic field. Suppose at some time the electric field arrow points to the right. As you watch, it gets shorter and shorter until it momentarily vanishes and then grows in the opposite direction to the left to the same length. Then it starts getting smaller again until it sloshes back to its original position. Meanwhile the other arrow, the magnetic field arrow at right angles, is sloshing upwards and downwards in a similar fashion.

Note that you are to imagine the arrows as NOT extending in space around the point - they really correspond to moment-by-moment meter-readings of the field strengths constituting the wave at exactly that point.

[Note this corresponds to a plane-polarised wave - I'm trying not to make it too complicated].

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Thanks, this really helped me picture it! –  Ell Jan 21 '11 at 18:00

There is a subtlety to be considered in these discussions on EM waves.

In Classical Electrodynamics the E and B fields (electric and magnetic) are vector functions of space (and time). So E is E( x) for example, and can be measured throughout space. This is how the theory is introduced as well in elementary texts.

Maxwell's equations are equations for E( x) and B( x) and so the solutions (the waves) are also functions of x. Thus the solutions describe waves in space and time. The diagrams and pictures linked in the other Answers well display these wave solutions.

The complication is that one also has quantum theory - which replaces all classical theories as the "correct" framework for physics. In the replacement of Electrodynamics we have Quantum Electrodynamics. The key difference is that it introduces abstract spaces (called Hilbert Spaces) and abstract mathematical objects in them. "Abstract" here means that these are not spacetime objects, but only indirectly get measured at spacetime points. So what happens is that the E and B become abstract entities called "operators" which are measured at each spacetime point (or region). These E and B operators obey algebraic laws - which turn out to be just Maxwell's equations in this format. So the wave solutions describe abstract objects (which can nevertheless be measured) associated with each point, rather than actual wave movements in the real x and y directions as the classical theory would have us believe.

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Although a little bit complicated for my level, this still helped and was very interesting, thanks! –  Ell Jan 21 '11 at 18:04