  The classical theory of electrodynamics cannot explain the existence and
structure of electric and magnetic dipoles, yet it incorporates such dipoles
into its fundamental equations, simply by postulating their existence and
properties, just as it postulates the existence and properties of electric
charges and currents. Maxwell's macroscopic equations are mathematically exact
and self-consistent differential equations that relate the electromagnetic (EM)
field to its sources, namely, electric charge-density $\rho_{free}$, electric
current-density $J_{free}$, polarization P, and magnetization M. At the level
of Maxwell's macroscopic equations, there is no need for models of electric and
magnetic dipoles. For example, whether a magnetic dipole is an Amperian
current-loop or a Gilbertian pair of north and south magnetic monopoles has no
effect on the solution of Maxwell's equations.
  Electromagnetic fields carry energy as well as linear and angular momenta,
which they can exchange with material media - the seat of the sources of the EM
field - thereby exerting force and torque on these media. In the Lorentz
formulation of classical electrodynamics, the electric and magnetic fields, E
and B, exert forces and torques on electric charge and current distributions.
An electric dipole is then modeled as a pair of electric charges on a stick (or
spring), and a magnetic dipole is modeled as an Amperian current loop, so that
the Lorentz force law can be applied to the corresponding (bound) charges and
(bound) currents of these dipoles. In contrast, the Einstein-Laub formulation
circumvents the need for specific models of the dipoles by simply providing a
recipe for calculating the force-density and torque-density exerted by the E
and H fields on charge, current, polarization and magnetization.
