The magnetic field inside special conducting geometries due to internal current

In view of recent attempts to directly and noninvasively detect the neuromagnetic field, we derive an analytic formula for the magnetic field inside a homogeneous conducting sphere due to a point current dipole. It has a similar structure to a well-known formula for the field outside any spherically symmetric conductivity profile. For a radial dipole, the field on the inside has a very simple expression. A symmetry argument is given as to why the field of a radial dipole vanishes outside a spherical conductor. Illustrative plots of the magnetic field are presented for a radial and a tangential dipole; the slope of the tangential component of the magnetic field is discontinuous at the surface of the sphere. A spherical conductor having three concentric regions is discussed; and we also derive an analytic formula for the magnetic field inside a homogeneous infinite half space.