TABLE OF CONTENTS A conspicuous and eye-catching aspect of the four Maxwell equations is a certain symmetry they exhibit between electric and magnetic fields. But it is also obvious that this symmetry is violated if one looks at charge and current densities. This symmetry is described as duality. In this chapter we consider attempts to gain some understanding of these observations.
In our treatment of the Aharonov-Bohm effect we also encountered singular fields. A deeper investigation into such fields leads to the topic of magnetic monopoles, i.e. to that of single magnetic poles. The full symmetrisation of the Maxwell equations also requires the introduction of these monopoles.
We first recapitulate the Maxwell equations with new notation for charge and current densities to which we affix an index "e" for "electric":
and the equation of continuity is
Thus, as far as these Maxwell equations are concerned, there are electric charges as sources of the electric field, but no magnetic charges or poles as sources of the magnetic field, which are here provided by electric currents.
The equation ?. B = 0 has no source term. This asymmetry of the equations is not appealing. It is therefore a natural step to introduce magnetic poles and to completely symmetrise the Maxwell equations and to explore the consequences which result from this. For symmetry reasons it is helpful in this case to use the formulation in terms of the MKSA-units as we do here, and not Gaussian...
