- #71
Jano L.
Gold Member
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But there is no noticeable increase in the radiation energy. (v<<c)
If the electromagnet radiates isotropically in its frame (if it has symmetric shape), the energy radiated into all directions per unit time is Lorentz invariant; it is the same in all frames. Let's say the electromagnet radiated 1 J in one second, in its own frame of reference.
What is important, is that in the frame of the coil, the electromagnet is moving towards it. When a source of isotropic radiation moves in some direction, the radiation is released preferentially to that direction. Check
https://en.wikipedia.org/wiki/Synchrotron_radiation
The bunches of charged particles circling in synchrotron move so fast that the radiation is needle-like, similar to laser, only much brighter and not monochromatic.
With the electromagnet, it is similar; even if it moves slowly, there is more radiation going to the coil than in the other directions.
As the velocity is increased, coil receives greater and greater power. However, there is a limit: when v approaches c, the coil receives almost all the radiated power 1 J/s and this is the maximum. Of course, as the processes in the source are slowed down (dilatation) , it will receive it for a long time and thus the net amount of energy received in the end can be much greater than 1 J.
Where did the extra energy came from? From the total energy of the electromagnet; as the net energy of the electromagnet decreases by radiation, in the frame of the coil the electromagnet loses also momentum via loss of its mas (the velocity is unaffected).