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Physics, Astronomy & Cosmology / What's the paradox involving two moving parallel electrons?

« on: 07/06/2008 16:08:19 »

To rephrase what everyone else has said (broken down into steps)

(1) Special relativity tells us that if put an experiment on a train and run it past our observer at high speeds, he sees the experiment happening more slowly than it would appear to if the train is still.

(2) In order to test this paradox, we put two electrons on a table on the train some distance apart.  To someone onboard the train with them, they appear to repel entirely because of electrical forces since they're sitting still onboard the train.  They therefore move apart.

(3a) To an observer outside the train, because the experiment appears to slow down (special relativity), the electrons appear to move apart more slowly.  However, he can explain this entirely by understanding the electric repulsion on the train and then applying relativity to slow the effects down.

(3b) If the outside observer doesn't know about relativity (and electromagnetism was formulated before relativity), he can explain the "slowing down" as a result of the magnetic fields/forces that are generated by the motion of the electrons which oppose the electric "push" apart.

(4) The paradox is: if you use the magnetic field explanation instead of relativity, why does one observer see a magnetic field and the other not?  How can a field just vanish like that?  The resolution is that magnetic fields have a deep connection to relativity, and that you can describe the situation here without them if you understand the relativity going on.

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Question of the Week / Re: QotW - 07.12.09 - Power Source for Magnets?

« on: 07/12/2007 04:09:21 »

Every electron in the metal acts as a magnetic dipole.  Dipoles are the simplest sources of magnetic fields.  In order to generate a permanent magnet form a metal, you force all these dipoles to line up, so the tiny fields they each generate all add together to make a big field. 

If you stick this magnet to a fridge, I think the fields from the magnet should cause the electrons in the field to line up in an opposite direction.  This means if you have the north pole of a magnet near a fridge, the fridge will start to act like a south pole, and viola--your magnet will stick to your fridge.  If you try to push two like poles of magnets together, they repel because the electrons in each magnet are already aligned to repel each other and won't change direction easily. 

Finally, in terms of energy.  In physics, change in energy is defined as a force applied over a distance.  If you hold two magnets near each other until your arms get tired, you're not actually putting any energy into the magnets.  Similarly, by holding the magnets near each other, you're not getting energy out.  To get energy out, you'd probably have to let the magnets fly apart and use that motion to generate electricity or move something.  The simple reason why that isn't practical is that you have to put the same amount of energy into the system in the first place in order to put the magnets near each other!