# Electromagnetic Waves

nipiano93
We all know that Earth is rotating. So every particle on it is accelerating. So all the charges present on it are accelerating. So why there is no production of elecrtomagnetic waves by them? (As accelerating charges produce EM waves)

Gold Member
I always figured that the Earth's magnetic field was part of this "production of eletromagnetic waves" that you're talking about. But that's just my extremely amateurish guess that in no way should be regarded as fact.

nipiano93
take it like this. There is an observer with a charge on earth. He should see EM waves being produced as the Earth is rotating (and revolving of course). But he doesn't see any EM waves until the charge accelerates with respect to him. This thing is confusing me a lot. Please Help.

It's not true that accelerating charges inevitably lead to radiation. Charge separation within the rotating Earth is one theory of how the Earth's magnetic field is generated.

nipiano93
@BILL K
I'm not talking about Earth's magnetic field. What I'm talking about is the production of EM waves due to centripetal acceleration. And please explain how accelerating charges do not always produce em waves...

Mentor
Consider a variation of your question: A small stone contains electric charges. Tie a string to the stone and whirl it around, above your head. Why don't you get electromagnetic radiation from it?

Hint: the stone contains equal amounts of positive and negative charge, which produce E fields in opposite directions, likewise for the B fields. What are the net E and B fields?

Stretto
Um, there are EM waves produced! This is a well known phenomena.

http://en.wikipedia.org/wiki/Larmor_formula

If you calculate the power for a single electron it is extremely small. It is on the order of about 10^-50. Given the air density of about 1 it would mean we would require 10^50 m^3 of air to get 1W of power dissipation. This is for 1 electron in a m^3. The volume of the Earth is about 10^12. So we can have around 10^38 charges particles per m^3 which we can say is about 2C of charge.

So as you can see the actual radiation emitted is extremely small. Just around 1W for a huge volume due to all the charged particles flying around. Even if I were off by a factor of 10^10 and it would be relatively a small amount of power radiated per m^3(and this is using the Earth's volume as a reference which is going to be smaller than that of the atmosphere).

In any case these charged particles just don't spontaneously happen. They are due to outside sources which generally are going to have much more power that what generates these charged ions. The atmosphere of the Earth gets about 1.36kW/m^2 and the surface about half that. This means the atmosphere is absorbing that energy as it travels through. Say about 500W is absorbed in the volume from the end of the atmosphere, about 120km, to the surface, about 6km. This has a volume of about 120k m^3. This means that each unit volume is absorbing about 500/120k ~= 5W/m^3 which is 5 times what I estimated using the Earth's volume.

The main point is, is that energy does radiate from accelerating charges but it's quite small and insignificant for most things. The calculations above involve a lot of assumptions but even if one is off a few orders of magnitude it won't change the fact that the power radiated by an accelerating charge is very small(which means it's hard to detect).

Also you have to realize that the atmosphere does not spin just as fast as the Earth and as we get further out the particles are rotating slower and slower. This creates a complex EM field that needs a lot of theories to be able to accurately describe it(Fluid dynamics, Maxwell's equations, QM, etc...).