Accelerating charged particles and conservation of energy

[dgnunch]

Hi I'm wondering how when a charged particle is accelerating it both emits energy in the form of em radiation while also gaining kinetic energy. All of that energy comes from the thing accelerating the charged particle, yeah? Is that necessary, like it is not possible to give a charged particle kinetic energy without letting it "donate" some of it to the em radiation? Conservation of energy in terms of both the sun emitting energy via nuclear fusion and "bremsstrahlung" make sense to me.. but what dictates how much energy gets donated to the em waves and how much to kinetic? Like it seems arbitrary?

Thank you for your time

 

[Nugatory]

A long and unnecessary argument has been removed from this thread.

Please, everyone, if a post is inconsistent with the forum guidelines about helpfulness and civility... report it so that the mentors can take care of it.

 

[Nugatory]

Hi I'm wondering how when a charged particle is accelerating it both emits energy in the form of em radiation while also gaining kinetic energy. All of that energy comes from the thing accelerating the charged particle, yeah?

Yes. The energy expended to accelerate a charged particle is the sum of the increase in kinetic energy and the energy that is radiated away.

Is that necessary, like it is not possible to give a charged particle kinetic energy without letting it "donate" some of it to the em radiation?

Not possible (at least not in the context of this thread). The electrical field around the particle must change when it is accelerated because we are moving a charged particle around. Electromagnetic radiation is the way that change propagates, so it has to be present.

Conservation of energy in terms of both the sun emitting energy via nuclear fusion and "bremsstrahlung" make sense to me.. but what dictates how much energy gets donated to the em waves and how much to kinetic? Like it seems arbitrary?

Calculating exactly how much energy goes into radiation and how much goes into kinetic energy change will depend on the details of your particular setup. But it's not arbitrary: if you say that we have a charged point particle moving with a given acceleration along a given path we can in principle calculate exactly what the radiation emission will be.

 

[sophiecentaur]

Like it seems arbitrary?

Not "arbitrary", surely. The theory will tell you just how the Energy is shared.
There are other, more homely, apparent paradoxes about Energy transfers - such as where the energy goes when you connect a charged capacitor to an uncharged capacitor of the same value. And why, however fast or slow you choose to charge a capacitor, you 'waste' as much energy as you have put into the capacitor.