Use of electromagnetic scalar potentials in boundary value problems

Abstract

Expressions for the electric and magnetic fields in terms of scalar potentials are derived, and boundary conditions that the scalar potentials obey at dielectric interfaces and at conducting surfaces are discussed. The relationship of the scalar potentials to source charges and currents is described. It is shown that scalar potentials can be defined that do not obey the wave equation, but the source charge and current configurations that can be associated with such potentials are more limited than those that do obey the wave equation. Examples are given of the use of electromagnetic scalar potentials in boundary value problems.

Metamaterial Eigenmodes beyond Homogenization

“…2. The physics is naturally richer for the TM modes, where the fundamental dipole Mie resonance (the first pole of the scattering coefficients [43,44]) of the individual cylinders lies in the frequency range of interest. Within a small band close to this dipole resonance, the constant current approach is insufficient.…”

Multipole Analysis of Circular Cylindircal Magnetic Systems

“…This should be extended to include a dynamic formulation. There is no theoretical reason prohibiting the application of the Q-function to electrodynamic problems such as, radiation [108,109], eddy currents [110,111,112], time varying electric and magnetic fields [113,114,115], etc. Also, one can employ the Q-function formulation for computing electromagnetic forces in cylindrical coils [116,117].…”

Analysis of off-axis solenoid fields using the magnetic scalar potential: An application to a Zeeman-slower for cold atoms

“…Sadly, most students do not usually appreciate the similarities between the two classes of problems 8 due to a limited exposure to practical examples involving the magnetostatic potential. We feel that this ability is useful 9 , particularly because scalar potentials are generally more intuitive and easier to visualize.…”

“…We begin here by recalling the fundamental equation of magnetostatics : However, despite the obvious similarities between the electrostatic and magnetostatic potentials, there are indeed reasons why the analogy can only be taken so far 8,10 , and is not widely explored further in textbooks. The first one arises whenever − → J = 0, in which case it is not trivial to write a relation between φ M and − → J .…”