Analytic Solution of the Magnetic Field and Inductance in a Coaxial Short Circuit

In this paper, the analytic solution of the magnetic field and the inductance in a coaxial short circuit is derived from Maxwell's equations with the appropriate boundary conditions on the short circuit. Helmholtz equation is thus derived for the magnetic field and is solved by a mode matching technique. By integrating the absolute square of the magnetic field the inductance is obtained. The solution is discussed in the light of earlier approximations and solutions and is evaluated both theoretically and through measurements.