Abstract

It has previously been shown that a surface current density J on a closed surface Σ of class C^∞ in R³ induces a static magnetic field B_J in R³ Σ, which has some discontinuity along Σ. In this note, we represent B_J by use of jump theorem for harmonic forms in the case where Σ is of class C^ω. We then apply this result to prove the existence of a surface current density J, which induces the nonzero magnetic field B_J such that B_J ≡ 0 inside (or outside) of the domain bounded by Σ in R³, which has previously been called the equilibrium magnetic field for Σ.