(a) Show that the electromagnetic linear momentum PEM for static fields in all of space can be rewritten in terms of the current density j(r) and the electrostatic potential ϕ(r).
(b) Point charges q and −q sit at points (0, 0, d) and (0, 0,−d), respectively. A point magnetic dipole with moment m sits at the origin. Show that PEM = E(0) × m/c², where E(0) is the electric field of the charges evaluated at the origin.
(c) A point electric dipole with moment p sits not far from a steady distribution of current. Express P_EM in terms of p and the Coulomb gauge vector potential.