Helical Fields

Abstract

This paper is devoted to a study of helical fields, that is fields which are invariant under screw motions of space which move a certain helix into itself. Simple, analytic, helically invariant solutions of the Laplace equation are given and combined to describe the electrostatic field of a charged helix, and of the magnetic field of a helical electric current. A flux function ψ is introduced for solenoidal helical vector fields, and differential equations resembling Cauchy‐Riemann equations are derived for the potential function φ and the flux function ψ. Certain graphical flux plotting methods are outlined and illustrated, and network analogies are suggested for solving these fields.