How Does a Magnetic Field Possess Angular Momentum?

[SpitfireAce]

I was reading Feynman's "Character of Physical Law" and in it he discusses how conservation of angular momentum is seemingly broken when you take a magnet and bring it through the center of a conductive disk... there is an induced electrical current and if the disk was on wheels it would spin... angular momentum from nothing... after that he says that the angular momentum actually is conserved because the magnetic field has an angular momentum of opposite spin... I didn't get this explanation, the magnetic field lines would curl in the same direction as the disk's spin right? how can a field have an angular momentum?

 

[Nesk]

My guess would be that by bringing the magnet through the disk, a current is induced so that a force acts against the movement of the magnet. Moving the magnet through the disk thus involves some work against this force, and the system is therefore not isolated. Laws of conservation usually presuppose an isolated system, and thus do not apply here.

As I said, it is only my guess, though it might prove equivalent to the explanation you quote.

 

[Loren Booda]

I suppose that the phenomenon Feynman was referring to has to do with "back EMF," which in the case of a motor may maintain the relative rotation between its armature and the magnetic field driving it.

 

[mdelisio]

E-M fields carry both energy and momentum. The momentum density field points in the same direction as the Poynting vector (E cross H), and there can be angular momentum in the fields as well.

David Griffiths has some great examples in his Intro to Electrodynamics if you have access to that.

 

[meopemuk]

I was reading Feynman's "Character of Physical Law" and in it he discusses how conservation of angular momentum is seemingly broken when you take a magnet and bring it through the center of a conductive disk... there is an induced electrical current and if the disk was on wheels it would spin... angular momentum from nothing... after that he says that the angular momentum actually is conserved because the magnetic field has an angular momentum of opposite spin... I didn't get this explanation, the magnetic field lines would curl in the same direction as the disk's spin right? how can a field have an angular momentum?

There are lot of controversies in classical explanations of interactions between magnets and charges. For example, these explanations require that static electric and magnetic fields have non-zero momentum and angular momentum. Moreover, they lead to the notions of "hidden" linear and angular momentum in material bodies. Take a look at the following papers (and numerous references therein), where authors painfully try to make sense of these ideas:

S. Coleman, J. H. Van Vleck, "Origin of "hidden momentum" force on magnets", Phys. Rev. 171 (1968), 1370

W. H. Furry, "Examples of momentum distribution in the electromagnetic field and in matter", Am. J. Phys. 37 (1969), 621.

R. H. Romer, "Angular momentum of static electromagnetic fields", Am. J. Phys. 34 (1966), 772

G. Spavieri, G. T. Gillies, "Fundamental tests of electrodynamic theories: Conceptual investigations of the Trouton-Noble and hidden momentum effects", Nuovo Cim. B 118 (2003), 205.

Eugene.