I was thinking about a situation: In space there is our setup, a wood piece of mass $m$ and a coil and permanent magnet of mass $m$. The coil is placed a light second far from the magnet. The magnet is now given a force to move with a velocity $V$ (let's assume 100m/s).

After half of a second the magnet strikes with the wood block and loses all its velocity. All the kinetic energy of the magnet is gained by the wood (which is not a magnet).

But we know that the magnet was also releasing magnetic fields. And when it started moving, there was a changing strength of magnetic field produces that reaches the coil after 1sec (the coil was 1 light second far in space).

Is this not violating conservation of energy as all of the mechanical energy given to magnet (in the system) was gained by the wood. But due to the velocity of the magnetic field the magnetic field had not reached the coil in given time (before the magnet loses its K.E.), so they can't produce any of their own magnetic field caused by induced current and therefore can't affect the magnet in that given time.

But to add to this, when there is current induced in coil after 1 sec, it's magnetic field produced forces the magnet to move.

Main highlights:

So we are only putting $mv^2/2$ energy which was transferred from magnet to the wood by collision but there comes extra output which is current induced in the coil and magnet's motion, why is it not a violation to law of Conservation of energy?

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    $\begingroup$ Related post by OP: physics.stackexchange.com/q/645032/2451 $\endgroup$
    – Qmechanic
    Jun 13 at 11:27
  • $\begingroup$ @Qmechanic That last post was having too much complication with it that it was misleading in some ways. That's why i created a new question using a magnet instead of battery powered coil to focus on the main thing $\endgroup$ Jun 13 at 11:42
  • $\begingroup$ What this question about? $\endgroup$ Jun 13 at 13:02
  • $\begingroup$ Question is to explain how the situation given above is not a violation to conservation of law of energy $\endgroup$ Jun 13 at 16:24

So we are only putting $mv^2/2$ energy which is gained by the wood but the extra output is current induced in the coil and magnet's motion, why is it not a violation to law of Conservation of energy?

Actually, due to the magnetic radiation reaction force, the energy required in order to accelerate the magnet to $v$ is greater than $mv^2/2$. See https://en.wikipedia.org/wiki/Magnetic_radiation_reaction_force

The radiation released by accelerating the magnet acts as a sort of magnetic drag force that makes it more difficult to accelerate the magnet than it would be to accelerate a non-magnetic item of the same mass. This is similar to the well known Abraham-Lorentz force for electrically charged particles.

  • $\begingroup$ You are saying that the energy in motion of magnet was little less than $mv^2/2$ thinking that the radiation was given off by it. But if we assume that all other objects in the space are moving with $v$ velocity just as the magnet and only the coil was having 0 velocity then, only coil can get the energy released and all radiation given off in other direction will not be absorbed by anything $\endgroup$ Jun 13 at 16:31
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    $\begingroup$ @PredakingAskboss said “You are saying that the energy in motion of magnet was little less than 𝑚𝑣2/2”. No, the KE of the magnet is indeed $mv^2/2$. But it takes more work than $mv^2/2$ for the magnet to reach that KE. The additional work is the energy in the radiation. The initial reference frame doesn’t matter. The acceleration takes more work in all frames $\endgroup$
    – Dale
    Jun 13 at 16:39
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    $\begingroup$ @PredakingAskboss absolutely. The energy is in the EM radiation itself, regardless of whether it eventually gets absorbed by some other object. $\endgroup$
    – Dale
    Jun 13 at 16:44
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    $\begingroup$ @PredakingAskboss the energy would still be released even without the coil and regardless of how many coils you use you can never extract more energy than is in the EM radiation. That is a direct result of Poynting's theorem $\endgroup$
    – Dale
    Jun 19 at 19:54
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    $\begingroup$ @PredakingAskboss please ask that as a new question $\endgroup$
    – Dale
    Jun 20 at 11:16

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