Magnetic field of a current ring

An expression for a magnetic field of a current ring is presented. The current distribution in the cross section of a thin current ring is expressed as a two-dimensional delta function and is substituted in Poisson’s equation for vector potential. The expression, derived from the solution of the equation, is given in the form of an integral with respect to a parameter. The expression is applied to the problem of the magnetization current on the surface of an iron core and to the problem of the self-inductance of an air-core coil.