Electromagnetic systems always dissapative?

[HomogenousCow]

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?

 

[Arkavo]

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?

 

[HomogenousCow]

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?

 

[Blue chocolate]

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.

 

[HomogenousCow]

I am talking about electrodynamics, potentials are not well defimed here
accelerating charges will radiate away their energy

 

[vanhees71]

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

 

[HomogenousCow]

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?

 

[Jano L.]

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.