It has previously been shown that a surface current density J on a closed surface § of class C1 in R3 induces a static magnetic ¯eld BJ in R3 n §, which has some discontinuity along §. In this note, we represent BJ by use of jump theorem for harmonic forms in the case where § is of class C!.We then apply this result to prove the existence of a surface current density J, which induces the nonzero magnetic ¯eld BJ such that BJ ´ 0 inside (or outside) of the domain bounded by § in R3. This has previously been called the equilibrium magnetic ¯eld for §.