Accelerating charged particle radiation reaction

In summary, the conversation discusses the concept of charged particles emitting electromagnetic waves when accelerated. This means that not all of the work done on the particle goes towards its kinetic energy, and Newton's F=ma does not fully apply for charged objects. The effect of this is negligible in practice, but it can be seen in situations such as antennas or a negatively charged sphere orbiting a positively charged sphere. However, this issue is not fully solved in classical electrodynamics and is a difficult problem to understand.
  • #1
roboticmehdi
34
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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 can't find peace if i don't understand it properly.
 
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  • #2
hi roboticmehdi! :smile:

(try using the X2 button just above the Reply box :wink:)
roboticmehdi said:
… 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?

that's correct :smile:

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! :wink:
 
  • #3
tiny-tim said:
hi roboticmehdi! :smile:

(try using the X2 button just above the Reply box :wink:)


that's correct :smile:

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! :wink:

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
roboticmehdi said:
i think it is not negligible, for example in antennas, which try to deliver as much work as possible to electromagnetic waves,

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

what would be the body with mass m in that equation? :confused:
and for example a negatively charged sphere orbiting positively charged sphere of much bigger mass …

"orbiting"? how would that happen?
then there are particle accelerators

again, we don't use F = ma, we use more complicated field equations
 
  • #5
tiny-tim said:
but we wouldn't use F = ma for an antenna …

what would be the body with mass m in that equation? :confused:

electrons are accelerated in antenna by electric field in the conductor. that electric field applies force on electron and it accelerates. electron has mass. so theoreticly it is possible to apply F=ma. to make things simpler you can assume the conductor to be a superconductor so that there is no resistance of wire to electrons. its like ignoring air resistance and making the environment airless, i.e. vacuum.


"orbiting"? how would that happen?

the same way as Earth orbits sun. the negatively charged sphere would be attracted to positively charged sphere. having the right initial velocity, it would circle around positively charged sphere. but of cource the orbit would decay and lose all energy to electromagnetic waves. the circling body would eventually fall on positively charged sphere.


again, we don't use F = ma, we use more complicated field equations

ok maybe not F=ma here but definitely F=d(mv)/dt
 
  • #6
i don't how to do this sorry. in my upper post some of my comments are inside the quoted text. don't miss it.
 
  • #7
anybody has other answers to my question ?
 
  • #8
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
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.

The best source to learn about this difficult problem is the book

F. Rohrlich, Classical Charged Particles, World Scientific 2007
 

FAQ: Accelerating charged particle radiation reaction

1. What is "accelerating charged particle radiation reaction"?

"Accelerating charged particle radiation reaction" refers to the phenomenon where a charged particle accelerates and emits electromagnetic radiation as a result of its interaction with an external electric or magnetic field.

2. How does accelerating charged particle radiation reaction occur?

When a charged particle is subjected to an external electric or magnetic field, it experiences a force that causes it to accelerate. As the particle accelerates, it emits electromagnetic radiation in the form of photons.

3. What are the applications of accelerating charged particle radiation reaction?

Accelerating charged particle radiation reaction has various applications in fields such as medical imaging, particle accelerators, and nuclear energy. It is also used in the study of atomic and subatomic particles.

4. What is the role of radiation reaction in particle accelerators?

In particle accelerators, radiation reaction plays a crucial role in the control and manipulation of charged particles, as well as in the production of high-energy radiation beams for various applications.

5. How is accelerating charged particle radiation reaction related to relativity?

According to Einstein's Theory of Relativity, a moving charged particle experiences a change in its mass and energy, which affects its acceleration and radiation emission. Therefore, accelerating charged particle radiation reaction is closely related to the principles of relativity.

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