(a) Show that the angular momentum of an electromagnetic field in empty space (no sources) can be written in the form

Note any requirements that the fields must satisfy at infinity. The last term is assigned to Lspin because it is a contribution to the angular momentum that does not depend on the “lever arm” r.
(b) Show that the proposed decomposition is not gauge invariant and therefore not physically meaningful.
(c) Despite the foregoing, work in the Coulomb gauge and apply these formulae to a circularly polarized plane wave with electric field

Show that the time averages obey ± ω ẑ · (L_spin) = (UEM). Interpret this formula if (U_EM) = − hω.

Transcribed Image Text:

LEM = €0 d³rr × (E × B) = €o √ √d³r Ex(r × V)Ak + €0 to [d³r Ex A = d³r ExA= Lorbital + Lspin.