Expressions for the field line equations in potential fields

摘要

Construction of field lines for vector fields can be performed by a variety of analytical or graphical methods. Except for a small number of simple geometries, where closed analytical expressions can be obtained, the shape of the field lines is determined by numerical computation or evaluated approximately by physical modelling techniques [1]. In this paper, we consider irrotational vector fields that are derived from scalar potential functions and expansions are obtained for the field line equations valid in the neighbourhood of any point at which the potential and its derivatives are defined.