Boundary conditions for small displacements in a magnetic field

When mechanical displacements occur in the presence of a magnetic field, the movement of the material boundaries causes a change in the field throughout the system. In a linear perturbation analysis, the effect of small boundary displacements can be duplicated by leaving the material undisturbed and introducing instead a combination of currents an~l magnetic charges on the boundary surfaces. The specific nature of these sources is eml~odied in two boundary conditions which must be satisfied by the perturbation magnetic field. These relations are derived for both smoothly deformed surfaces and sharp edges. Since these expressions directly equate perturbation quantities, their use bypasses the error-prone lineaxization process.