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Instead of broadening up the scope of answer , I would like to divide this question into two parts without any introduction .

1) Do all the time varying EM fields have the ability to transfer energy ?

2) Let us consider a charged particle moving with uniform velocity . It can create time varying EM fields too . Now let us consider an accelerating charged particle , it creates time varying EM fields too and transmits energy . What are the basic points of difference between the ways in which energy is transferred in these two cases ??

Agnivesh Singh
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  • Every EM field contains energy and momentum. The difference is that time varying fields radiate. A free particle moving creates a field that varies in space because the particle is moving, but it doesn't radiate. The accelerated particle will lose energy because the fields produced by it really are varying, even in the particle's own reference frame. – QuantumBrick Mar 20 '15 at 17:59
  • @QuantumBrick : Isn't radiation same as transferring ? – Agnivesh Singh Mar 20 '15 at 18:01
  • Is it? I don't know. What's you definition of transferring? A charged capacitor is an example of stored energy that doesn't radiate... – QuantumBrick Mar 20 '15 at 18:03
  • @QuantumBrick : Take the case of a static electron . Suppose we can ensure that it remains firm at its position irrespective of the movement of other particles on whom it is exerting forces . And what about the case of an electron moving with uniform velocity as in the question ? – Agnivesh Singh Mar 20 '15 at 18:06
  • Both the static electron and the uniformly moving one won't radiate. Radiation depends on acceleration in these cases. – QuantumBrick Mar 20 '15 at 18:07
  • @QuantumBrick : So change of kinetic energy of a charged particle under the influence of a static charged particle is not the same as radiating ? I guess the uniformly moving one would also create time varying EM fields ..so why isn't that radiating ? – Agnivesh Singh Mar 20 '15 at 18:10
  • @QuantumBrick : What exactly would be defined as radiation of energy then ? – Agnivesh Singh Mar 20 '15 at 18:10

2 Answers2

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The website asks to avoid long discussions on the comment section, so I'll post my thoughts here.

1) Time varying EM fields radiate.

2) A particle moving with uniform velocity doesn't radiate. It needs to be accelerated. Take a look at Liénard-Wiechert potencials.

If you have a system where one charged particle is standing still and another one is orbiting it, the one in the center wont radiate, and the orbiting one will. It'll lose energy as it radiates and fall towards the center of the orbit. This was once a paradox in Old Quantum Theory.

Community
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QuantumBrick
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What you're looking for is the Poynting vector, which represents energy flux. It is defined as $$ \mathbf S = \mathbf E \times \mathbf H $$ Time variation in EM fields is not enough to transfer energy; you need perpendicular electric and magnetic fields.

For a derivation of this, I recommend the Wikipedia article on Poynting's theorem.

morrna
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