Radial Anisotropy Added to a Spherically Symmetric Conductor Does Not Affect the External Magnetic Field Due to Internal Sources

It has been shown previously that the magnetic field outside a spherically symmetric conducting body due to internal current sources does not depend on the profile of conductivity along the radius. It is demonstrated here that an arbitrary distribution of radial anisotropy superimposed on the symmetric conductivity, even if the spherical symmetry is broken, does not alter the magnetic field outside. This result simplifies the analysis of magnetic fields produced by the human brain.