The usual derivation of Maxwell's equations for magnetic materials rests on the assumption that the sources of magnetic field within the material can be split up into a magnetization density M and a current density j. In metals the same electrons (the conduction electrons) contribute both to M and to j, and one is forced to consider the question of what one means by M and what one means by j. In this paper we answer the question for systems in equilibrium, using a thermodynamic approach. The separation of sources of magnetic field into M and j is to a large extent arbitrary, but can be done in such a way that M is uniquely related to the local magnetic field and j is zero for a normal metal in equilibrium, while in the mixed state of a superconductor it satisfies the force-balance equation $\frac{(\mathbf{j}\times \mathbf{B})}{c}+\mathbf{P}=0\mathrm{}$, P being the pinning force. The stress tensor for a magnetic system is derived from first principles (not assuming the field equations), and used to obtain the force-balance equation by an alternative method. Finally, two-dimensional systems such as superconducting thin films and surface sheaths are examined by similar methods.

Close

PrevNext

View figure in article