EM Waves: How Do They Get Generated?

[torquerotates]

I read that em waves get generated by oscillating and/or accelerating charges. I am confused on how this occurs. Doesn't this violate energy conservation? Say 2 charges( a +& a -) are separated by a certain distance. So they have potential energy. Then you let them go. The potential energy is converted to kinetic energy. But if the potential energy is converted to kinetic, where does this leave room for em waves?

 

[Shooting Star]

According to classical electrodynamics, an accelerating charge has to radiate. The radiation has both energy and momentum, which comes at the expense of the KE and momentum of the charged particle. So, the charged particle will actually accelerate less than a neutral particle of the same mass under the same force. It’s as if the radiation is having a recoil effect on the charge. That solves your energy conservation problem, I hope.

 

[torquerotates]

But if you consider the system to be just the 2 charges, there is energy violation. Because there is no external force acting on the system. Unless the system now changes to the 2 charges plus the radiation. But I don't think that is allowed because the system defined in the first place is just the 2 charges(+a &-a).

 

[Shooting Star]

(Remember, according to classical electrodynamics, an accelerating charge has to radiate.)

Isolated charges only occur in the first chapter of elementary electrostatics textbooks. In reality, you have the two charges, and their fields filling the Universe (somewhat loosely speaking, of course.) The charges and the fields interact mutually, giving rise to EM radiation. I am trying to answer as simply as possible.

Suppose you put a body in vacuum, and define it to be an isolated body. But then it cools off, giving off infrared radiation. What will you say now? Is it still an isolated body, by your “definition”?

 

[torquerotates]

Yeah, that is what I'm confused about. So the initially defined system is just the isolated body. And the system after is still the same because the isolated body(previous)=the body+em energy. Therefore no external work is done on the system. And energy and momentum is conserved. Am I correct with this line of thinking ?

 

[Shooting Star]

But if you consider the system to be just the 2 charges, there is energy violation. Because there is no external force acting on the system. Unless the system now changes to the 2 charges plus the radiation. But I don't think that is allowed because the system defined in the first place is just the 2 charges(+a &-a).

The energy was already there, in a different form. Suppose an “isolated” bomb explodes, then the chemical energy just got converted into mechanical energy.

Isolated systems are mental constructs invented by scientists to study certain aspects of Physics without getting cluttered by non-essentials. For example, in thermodynamics, an isolated system may mean an insulated container which cannot exchange energy or matter with outside. In mechanics, isolated systems generally mean one on which no external force or torque is acting. But internal forces can always be there.

In the example I’d given, suppose we are only studying the angular momentum of the body (classically). Then it hardly matters whether the body cools off or not. But in reality, there is no system which is isolated.

Coming back to your original problem, your isolated system consisted of two charges. If the two charges interacted and produced EM radiation, it’s somewhat like the bomb exploding. The energy of EM radiation was already there as PE.

And the system after is still the same because the isolated body(previous)=the body+em energy. Therefore no external work is done on the system. And energy and momentum is conserved. Am I correct with this line of thinking ?

Yes.

 

[torquerotates]

Oh... I see. Thanks your last post was very insightful. I've been confused on how energy and systems work until you brought up your point about the virtual non-existence of isolated systems. Well, I've only taken mechanics and E&M. But not thermo yet.