# Accelerating a charged particle generating an "electric field wave"

1. Nov 14, 2015

### JaredMTg

Hello,

My question is about accelerating charges generating electromagnetic radiation, and is more of a theoretical one, or a thought-experiment in my head...probably because I'm not totally understanding something.

I was playing with this applet which simulates the electric field lines of a charged particle under different types of acceleration:

This led me to understand that "waves" in the electric field are basically created because a charged particle accelerates, which generates a change in its electric field - "compressions" and "rarefactions" in a sense - and the particle's infinitely-extending field throughout space cannot "update" instantaneously - i.e. there is a limit to the speed of propagation of the change (or "information") in the field, which we know to be the speed of light, c

My question is, is there anything inherent about the electric field that makes it unable for a variation in the electric field to propagate faster than the speed of light? I realize that Maxwell's equations indicate that a changing electric field generates a magnetic field, which is also non-constant and continues the propagation of the electric field. Therefore, any accelerating charge produces varying magnetic and electric fields which are inextricably linked, and due to the nature of permittivity and permeability of space, this process happens at the speed of light, c.

But suppose for a minute that you "de-coupled" the electric field from the magnetic one (even if no such thing is possible in reality), and tried to look at things the way they are shown in the applet above (i.e. without magnetic fields), and you understood "electric waves" as simply compressions and rarefactions in the electric field due to the disturbance of the charged particle's motion. Does the idea of an electric field wave in isolation correspond to anything in physical reality? And would it move at the speed of light?

2. Nov 14, 2015

### davenn

Hi Jared
welcome to PF

you answered your own Q ... what else can we say ?
As far as has been discovered, c is the "universal speed limit"
Why ? ... it just is

Dave

3. Nov 15, 2015

### JaredMTg

Hey, you're right - I did! How brilliant!

4. Nov 15, 2015

### BvU

It's not complicated unless you start thinking too much behind it (*): $c^2 \epsilon_0 \mu_0 \equiv 1$ . Hurray for good old Maxwell !

(*) But of course we all do (present author included ) -- and hopefully get put right by reality ! Whatever that is.

5. Nov 15, 2015

### BvU

Thanks for the phet link! I think I could have saved meself a lot of time spent drawing still pictures with links to their suitable and didactically well researched, much nicer animations !

"The name "PhET" was originally an acronym for "Physics Education Technology." However, the PhET site now includes simulations about many other subjects besides physics, so the acronym is too limited. The PhET team decided to keep the name because it is so widely recognized, but now it's just a name that doesn't stand for anything."

6. Nov 15, 2015

### Staff: Mentor

You cannot decouple the electric and magnetic fields this way, but you can decouple the scalar and vector potentials that way. They each separately follow wave equations that propagate at c.

7. Nov 15, 2015

### JaredMTg

Fair enough, makes sense. Thanks!