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Suppose we hold two bar magnets with opposite poles facing each other a certain distance away.

We let go and the magnets fly towards each other.

We observe that the magnets gain kinetic energy. Then work must have been done on their masses.

I am told that magnetic forces are always perpendicular to the velocity vector and hence cannot do work. But clearly here, the magnetic field has done work.

How can we reconcile the motion of the bar magnets with the statement about magnetic forces. I simply don't get it. If the magnetic field isn't whats providing the accelerative force, then what is?

Thanks :)

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    $\begingroup$ "I am told that magnetic forces are always perpendicular to velocity and hence cannot do work. But clearly here, the magnetic field has done work, undeniably." I think that you are thinking of the case of a charged particle going through a magnetic field. $\endgroup$ – Jimmy360 May 6 '15 at 22:59
  • $\begingroup$ Appar from Jimmy360 answer, variable magnetic field can do work as well. PS: I'm curious why somebody has downvoted this $\endgroup$ – Azad May 7 '15 at 7:36
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Yes, of course that if a field - magnetic field - is able to make a bar magnet rotate or move, it is doing work. The statement that magnetic fields don't do any work only applies to point-like pure electric charges. - Lubos Motl

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  • $\begingroup$ So the statement only applies to strictly electric charges? Ok, so for magnetic charges, or things with an "inherent" magnetic charge, work can be performed just like under an electrostatic field? So the case of the bar magnets is comparable to a huge positive and huge negative electrostatic charge flying towards each other? $\endgroup$ – Just_a_fool May 6 '15 at 23:09
  • $\begingroup$ @Just_a_fool yes $\endgroup$ – Jimmy360 May 6 '15 at 23:10
  • $\begingroup$ Thanks for the answer. That was pretty straightforward hehe. If its not too much to ask I have a few more questions: So for the case of an electron, is it both an electric charge and a magnetic charge. If yes, then how come when an electron enters a magnetic field, it performs uniform circular motion but does not spiral towards the positive terminal of the magnetic field (due to its magnetic-charge component). If no, then its pretty clear. Also, do pure electric point charges or pure magnetic point charges exist / are they experimentally observable? Thanks again :). $\endgroup$ – Just_a_fool May 6 '15 at 23:20
  • $\begingroup$ @Just_a_fool: There are no stationary pure magnetic point charges, as there are no magnetic monopoles. This may help: researchgate.net/post/… $\endgroup$ – Ernie May 6 '15 at 23:36
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    $\begingroup$ @Just_a_fool : a charged particle has an electromagnetic field. If you're motionless with respect to an electron you might say it has an electric field which causes linear force. If you then move, you would also notice rotational force, and you might say it has a magnetic field too. But you didn't generate a magnetic field for the electron just because you moved. It's the same when you move the electron. You don't create a new field, you merely reveal another aspect of the electromagnetic field. $\endgroup$ – John Duffield May 7 '15 at 7:23
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Suppose we hold two bar magnets with opposite poles facing each other a certain distance away. We let go and the magnets fly towards each other. We observe that the magnets gain kinetic energy. Then work must have been done on their masses.

I'm afraid not. You do work when you pull the magnets apart. That's when you add energy to the system. When you let go and they move towards one another, electromagnetic potential energy is converted into kinetic energy, which you can extract and use, but no new energy is added to the system.

I am told that magnetic forces are always perpendicular to the velocity vector and hence cannot do work. But clearly here, the magnetic field has done work.

It hasn't, not really. Yes we have a force and a distance, but there's no added energy.

How can we reconcile the motion of the bar magnets with the statement about magnetic forces. I simply don't get it. If the magnetic field isn't what's providing the accelerative force, then what is?

The interaction between electromagnetic fields, or more simply, the magnetic fields, do accelerate the magnets towards each other. Just like the Earth's gravitational field accelerates a brick. But you do work on the brick when you lift it, that's when the energy is added to the system, not when the brick falls down. Gravity merely converts potential energy into kinetic energy. When this is dissipated, you're left with a mass deficit, see Wikipedia. It's similar for the electron and proton, and for a pair of magnets.

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  • $\begingroup$ Thanks yea. I should have phrased my questions more along the lines of: "can work be stored between magnetic charges within a magnetic field, such that one can later extract work from the field" $\endgroup$ – Just_a_fool May 7 '15 at 10:09
  • $\begingroup$ LOL, pulling two magnets apart is a bit like a stretching a spring. $\endgroup$ – John Duffield May 7 '15 at 19:37

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