Energy principles for the confinement of a magnetic field

Energy is expended and stored when a vacuum magnetic field is confined to a limited volume of space. In the present paper this energy is analytically determined under conditions where the confinement is made quasi-statically by a perfectly diamagnetic medium. Special attention is given to a vacuum dipole field in the applications, but the established theorems apply to arbitrary superpositions of multipole fields as well. The energies required to confine the dipole field by a diamagnetic plane, sphere, hot plasma, and spheroid are explicitly calculated from the derived theorem. Of fundamental significance is the demonstration of how equilibrium boundaries can be predicted from a free surface variational principle based upon the proven energy theorem.