# How to visualize electromagnetic radiation

So I understand that light travels in waves and that they are fluctuations in the electromagnetic field and yada yada yada... but when I sat down and actually thought about it, I became confused.

Electromagnetic radiation is produced by charged particles; when electrons move, they create electromagnetic radiation that radiates outward in all directions. But I've also read that light travels in individual waves (ignoring the latter half of wave-particle duality). If light travels outward in all directions, like a sphere of fluctuating field that grows bigger and bigger at the speed of light, then how can this "sphere" also be composed of individual waves? It would require an infinite amount of individual waves! Which is correct? Is either correct? Are both correct?

Any additional information on the correct way to visualize EM waves is greatly appreciated!

• What's an "individual wave"? – NickD Jun 15 '17 at 4:11
• Electromagnetic radiation is a classical concept fitted with solutions of maxwell's equations. Wave-particle duality is a different story belonging to the quantum mechanical framework. Light is built up by zillions of photons in a complicated way, not just cutting up a classical wave into pieces. Maybe this illustration will help you en.wikipedia.org/wiki/Spin_angular_momentum_of_light – anna v Jun 15 '17 at 4:30

In the context of Classical Electrodynamics, the electromagnetic field is a set of vectors permeating space, 2 in fact, $\vec{E}(\vec{r}, t)$ and $\vec{B}(\vec{r}, t)$. These fields satisfy the Maxwell Equations.

From the Maxwell equations, you infer that a charges produces electromagnetic fields, which are described in general by the Lienard Wiechart potentials (true those potentials give very messy expressions, but they do accurately describe the electromagnetic field described by some charge moving around and doing stuff). When you further analyze those solutions, you notice that some of those fields carry net energy and momentum (by calculating the poynting vector) to infinity! Those are the so called radiation field generated by moving charges (note moving charges also produce induction fields in the near field etc... but they no not "travel" per se, or in our language carry net energy to infinity).

Now what we mean by "light" is those fields produced by those moving charges that go to infinity, aka those radiation fields. In other words, when we say the word "light" we usually mean fields of the form $\vec{E} (\vec{r}, t)$ that carry energy/momentum to infinity. One of those is the plane wave solution $$\vec{E} = E_0 \cos (\vec{k} \cdot \vec{r} - \omega t)$$

Those spheres that you mention are basically constant wavefronts, in other words iso-field surfaces that propagate to infinity. Light is not an individual wave as you say it. It is just a word that is used to describe particular solutions to Maxwell Equations in vacuum (or non-lossy media). Those solutions happen to look pretty and have wavefronts (constant field surfaces) propagating to infinity at the speed c, accurately named, the speed of "light"

So I understand that light travels in waves...

Electromagnetic radiation travels in packages called photons (and earlier quanta).

Electromagnetic radiation is produced by charged particles; when electrons move, they create electromagnetic radiation that radiates outward in all directions.

However you try to produce EM radiation you end up with the acceleration of subatomic particles. You can accelerate them forth and backwards or you can rotate them in circles. And even a body with room temperature consists of "shaking" particles and by this emits photons (in the range of infrared range).

About the direction of the emission you are not precise. In a particle accelerator ring the photons are emitted outwards the ring. In an antenna rod the photons are emitted perpendicular to direction of electron accelerations.

But I've also read that light travels in individual waves (ignoring the latter half of wave-particle duality).

As told above whenever you trace back to the source you'll see that EM radiation is made from individual photons from lots of subatomic particles. Since people are learned to synchronize the acceleration of electrons in an antenna rod we are able to observe the photons nature.

In the near field of the antenna we observe that an electric field induces a magnetic field induces an electric field of opposite to the last in direction induces a magnetic field in opposite to the last ... and so on. For a small volume it looks like this:

Any additional information on the correct way to visualize EM waves is greatly appreciated!

See this post about whot are photons, EM radiation an d EM waves.