The problem of an oscillating magnetic dipole at the centre of a lossless dielectric spherical shell is considered. For simplicity, the free-space wavelength is taken to be much greater than the shell radii, but the relative permittivity [epsilon][subscript r] of the shell is taken as much greater than unity, so the wavelength in the shell could be comparable with its dimensions. The vector potential in all regions is found. Under certain conditions, involving the shell radii, the frequency and [epsilon][subscript r], the vector potential outside the shell appears to be infinite. This is impossible, so one must conclude that the dipole moment vanishes. This result, a "disappearing dipole", although strange, can be justified. Although this paper is aimed primarily at readers with a strong interest in fundamental physics, it could be introduced as an interesting result in an undergraduate course on electromagnetism. (Contains 1 figure.)