# Accelerating charged particle radiation reaction

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1. Mar 20, 2012

### roboticmehdi

It is known that if a charged particle accelerates then it emits electromagnetic wave (energy). If so then this means that the work we do on particle, W=F*s, doesn't all go to particles kinetic energy, E=0.5*m*v^2. Then this means that Newton's F=m*a doesn't hold for charged objects, particles, masses, etc.. Is that true? If yes, then what resists particle to accelerate to the speed it deserves ( F*s=0.5*m*v^2, solve for v ). I hope i could explain my point. I am sorry i ask a lot about electromagnetism but it is so damn confusing to me, i cant find peace if i dont understand it properly.

2. Mar 20, 2012

### tiny-tim

hi roboticmehdi!

(try using the X2 button just above the Reply box )
that's correct

some of the work goes into the electromagnetic field, whose energy density increases

F = ma still holds, but you have to include the force from the field!

however, the effect is negligible in practice … a lot less than the air resistance which we also usually ignore!

3. Mar 20, 2012

### roboticmehdi

Why negligible? i think it is not negligible, for example in antennas, which try to deliver as much work as possible to electromagnetic waves, and for example a negatively charged sphere orbiting positively charged sphere of much bigger mass, the orbiting sphere would eventually lose all of its orbit energy to electromagnetic waves. then there are particle accelerators and etc. anyway, thanks for reply. can you tell me more about this ? or give good sources? what is that force acting on a particle? how it works ? thank you.

4. Mar 20, 2012

### tiny-tim

but we wouldn't use F = ma for an antenna …

what would be the body with mass m in that equation?
"orbiting"? how would that happen?
again, we don't use F = ma, we use more complicated field equations

5. Mar 20, 2012

### roboticmehdi

ok maybe not F=ma here but definitely F=d(mv)/dt

6. Mar 20, 2012

### roboticmehdi

i dont how to do this sorry. in my upper post some of my comments are inside the quoted text. dont miss it.

7. Mar 20, 2012

### roboticmehdi

anybody has other answers to my question ?

8. Mar 20, 2012

### chrisbaird

We don't typically use F = m a directly with electromagnetic waves, but it is still there in principle. We talk more in terms of energies than forces. The power radiated by an antenna, for instance, is not calculated as the force times velocity, but rather as the energy flow rate. The conservation of energy equation in electromagnetics accounts for both a force giving kinetic energy to a charged particle and also causing energy to radiate away.

9. Mar 21, 2012

### vanhees71

This is a problem that is unsolved in classical electrodynamics. Classical point particles interacting with their own radiation field leads to equations with weird properties, predicting among other things self-acceleration.