Angular Momentum of Static Electromagnetic Fields

A recently described “paradox” in classical electromagnetic theory is resolved by recognizing the fact that even a static electromagnetic field may have angular momentum. A charged particle, emitted from a source in a magnetic field, acquires a readily calculable angular momentum under the influence of the Lorentz force. The angular momentum of the static field after the emission of the particle can be independently calculated, and differs from its previous value by an amount which is exactly the negative of the angular momentum acquired by the particle. If the magnetic field is subsequently turned off, the field angular momentum which disappears is found to be exactly accounted for by changes in mechanical angular momenta. These results, although hardly surprising, provide a very clear illustration of the reality of field angular momentum, especially since the geometry is so simple that exact calculations can readily be made.