FOUR WAYS OF DEDUCING MAXWELL ’ S EQUATIONS FROM THEIR MICROSCOPIC COUNTERPARTS – LORENTZ ’ S THEORY OF ELECTRONS REVISITED

A century ago, Lorentz deduced the macroscopic Maxwell equations by spatially averaging a set of postulated Maxwell equations for the microscopic electromagnetic field. This averaging procedure is still relevant for obtaining the macroscopic behaviour of a medium from the interaction between the microscopic field and the particles of the medium. Crucial in this process is the identification of the average of the microscopic quantities in terms of macroscopic quantities. In this paper it is investigated how the choice of the microscopic magnetic field quantity and the magnetic dipole model affects the identification of the average of the magnetic field quantity.