Slovník pojmů

Vector potential

We introduce vector potential A in order to identically meet the fourth Maxwell equation

Since divergence of curl operation equals to zero, vector potential is defined as

Distribution of potential A uniquely determines the field B. On the contrary, a given field B is not uniquely related to a single potential A. If (1) if valid for a vector A, then the same relation is valid even for all vectors A '=A + grad y, where y is an arbitrary scalar function (curl of gradient identically equals to zero). The described ambiguity can be eliminated if an additional condition is formulated for A. Introduction of such condition is called calibration of a potential.

Physical notion of vector potential A is described by a relation defining the magnetic flux through the surface S

Obviously, the magnetic inductive flux through the surface S equals to the circulation of vector potential along the boundary curve of this surface.