According to every textbook I know of, magnetic forces do no work (e.g. David Griffiths Pg. 207). Yet this problem causes this to be hard to believe:

If I take two magnets, I can set them down on a table (with a little friction). I then slowly push them toward each other, then at some point, the two magnets attract and move toward each other on their own. That is, two magnets appear to exert a force on each other, and this force is exerted over the distance it takes to make contact (even with a little friction). Surly something is doing work to at least counteract the friction, if not cause non-zero mass magnets to move.

How can you tell me that magnetic forces do no work? These two magnets appear to do work, as far as I can tell.

This problem has bothered me for a long time. Please explain!

I have a response to this, but I think I'm going to wait and see if someone more math savvy than me can give him a better one, first.

“magnetic fields do no work without dissipating the field”

Changing the magnetic field changes the energy stored in the field, and changing energy implies work is being done or heat is being transformed.

From Stuart @ Stanford. http://stupac2.blogspot.com/2007/04/magnet...do-no-work.html

Even Wikipedia has "The magnetic force can do work to a magnetic dipole, or to a charged particle whose motion is constrained by other forces."
http://en.wikipedia.org/wiki/Magnetic_field

And the most exciting application of this is the Rail Gun.

http://en.wikipedia.org/wiki/Railgun