GENERALIZATION OF THE THOMSON FORMULA FOR HOMOGENEOUS HARMONIC FUNCTIONS

Abstract

It is shown that the Thomson formula for three-dimensional harmonic homogeneous functions can be generalized if, instead of purely algebraic linear expressions, one uses a linear algebraic form with the participation of the first order partial derivatives of the source function. The paper provides an exhaustive list of firtst order differentiating expressions that convert arbitrary three-dimensional harmonic functions, which is a homogeneous function in Euler terms, into new three-dimensional homogeneous harmonic functions.

Keywords

• electrostatic field
• magnetostatic field
• scalar potential
• homogeneous function
• harmonic function