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The classical theory of electrodynamics cannot explain the existence andstructure of electric and magnetic dipoles, yet it incorporates such dipolesinto its fundamental equations, simply by postulating their existence andproperties, just as it postulates the existence and properties of electriccharges and currents. Maxwell's macroscopic equations are mathematically exactand self-consistent differential equations that relate the electromagnetic (EM)field to its sources, namely, electric charge-density $\rho_{free}$, electriccurrent-density $J_{free}$, polarization P, and magnetization M. At the levelof Maxwell's macroscopic equations, there is no need for models of electric andmagnetic dipoles. For example, whether a magnetic dipole is an Amperiancurrent-loop or a Gilbertian pair of north and south magnetic monopoles has noeffect 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 EMfield - thereby exerting force and torque on these media. In the Lorentzformulation of classical electrodynamics, the electric and magnetic fields, Eand 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 (orspring), and a magnetic dipole is modeled as an Amperian current loop, so thatthe Lorentz force law can be applied to the corresponding (bound) charges and(bound) currents of these dipoles. In contrast, the Einstein-Laub formulationcircumvents the need for specific models of the dipoles by simply providing arecipe for calculating the force-density and torque-density exerted by the Eand H fields on charge, current, polarization and magnetization.

Electric and Magnetic Dipoles in the Lorentz and Einstein-Laub Formulations of Classical Electrodynamics