The Static Maxwell system in an Axially Symmetric Inhomogeneous Medium, an Axially Symmetric Generalization of the Cauchy-Riemann System with Variable Coefficients and New Generalization of the Complex Potential Method

Static meridional fields in some axially symmetric inhomogeneous media are studied using methods of modified quaternionic analysis in $R^3$. An axially symmetric generalization of the Cauchy-Riemann system with variable coefficients in $R^3$ plays a key role. New generalization of the complex potential method allows us to obtain surprising applications in modern problems of electrostatics and magnetostatics.