Electromagnetic systems always dissapative?

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    Electromagnetic Systems
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Discussion Overview

The discussion revolves around the behavior of charged particles in a vacuum, particularly focusing on whether electromagnetic systems are inherently dissipative. Participants explore the implications of energy radiation due to particle acceleration and the transformation of energy forms within the system.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants suggest that a continuous charge in vacuum will radiate energy away, leading to a loss of energy over time.
  • Others argue that while energy may be radiated, the total energy in the system remains conserved, as potential energy converts to kinetic energy during particle acceleration.
  • There is a discussion about the nature of energy loss, with some stating that the process is dissipative from the perspective of the particles, while the overall system's energy is conserved.
  • One participant raises a question about the behavior of particles after all initial energy has been radiated, seeking clarification on their motion and energy state.
  • Another participant emphasizes the complexity of understanding these phenomena within classical electrodynamics, noting that it has only been recently addressed in detail in literature.

Areas of Agreement / Disagreement

Participants express differing views on whether the energy loss constitutes a true dissipation of energy or merely a transformation of energy forms. The discussion remains unresolved regarding the long-term behavior of the particles and the implications of energy radiation.

Contextual Notes

Participants mention the limitations of defining potentials in the context of electrodynamics and the challenges in quantitatively understanding energy transformations in accelerated charged systems.

HomogenousCow
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Imagine a blob of continuous charge in vacuum, the fluid elements will exert a force on each other and thus radiate away energy to infinity and thus be forever lost, does this mean that charged continuums will always lose all of its energy?
 
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Well...
1) surface tension of the fluid in question will definitely hold it onto a certain level.
2) the fluid particles will perform work on each other so it would be reasonable to say that they will acquire Kinetic Energy. Intrinsic potential energy of the system will however be lost...

that's all i can say for now... can you give the the specifics of the problem?
 
Well for simplicity sake let's say you have n charged particles confined to some small region, they will exert a force on each other causing accelerations which in term causes energy to be radiated off to infinity. My question is, once all the energy at the start have been lost what will the particles do?
 
The amount of energy in the system will not change. The energy starts as potential (prior to release) and gets converted to kinetic (as the particles accelerate away from one another). It is not a matter of "losing" energy, but a change from potential to kinetic energy.
 
I am talking about electrodynamics, potentials are not well defimed here
accelerating charges will radiate away their energy
 
Accelerated charges radiate electromagnetic waves. From the point of view of the particles alone, the process is dissipative, because the charges loose energy when being accelerated. Of course the total amount of energy of a closed system of charges and the electromagnetic field is conserved. The energy lost by the particles is carried away by the (radiative part of the) electromagnetic field.

You should be warned that the quantitative understanding of this issue within classical electrodynamics is a very tough subject. It has been solved for practical purposes only quite recently. This is treated in great detail in the marvelous book

Fritz Rohrlich, Classical Charged Particles, World Scientific, 2007
 
vanhees71 said:
Accelerated charges radiate electromagnetic waves. From the point of view of the particles alone, the process is dissipative, because the charges loose energy when being accelerated. Of course the total amount of energy of a closed system of charges and the electromagnetic field is conserved. The energy lost by the particles is carried away by the (radiative part of the) electromagnetic field.

You should be warned that the quantitative understanding of this issue within classical electrodynamics is a very tough subject. It has been solved for practical purposes only quite recently. This is treated in great detail in the marvelous book

Fritz Rohrlich, Classical Charged Particles, World Scientific, 2007

Oh, so I'm assuming as t approaches infinity, the particles shoot off away from each other at constant speeds?
 
Well for simplicity sake let's say you have n charged particles confined to some small region, they will exert a force on each other causing accelerations which in term causes energy to be radiated off to infinity. My question is, once all the energy at the start have been lost what will the particles do?
Say we begin with n particles with charge of the same sign, initially kept still by other forces, and assume that fields are given by retarded solution of the Maxwell equations. Let's assume that the system has rest energy equal to sum of rest energy of the particles and the energy of the electrostatic field.

The particles will repel each other. After the constraints are removed, the particles will accelerate and produce radiation, which will propagate away to all directions. After a while, the particles will be all far away from each other, so the accelerations will be smaller. They will continue to move almost uniformly and will most probably retain some kinetic energy indefinitely. As a result, some energy has thus been transferred from the EM field to the kinetic energy of the particles.
 

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