The motion of a charged particle in a magnetic dipole has first been studied by Störmer. The different applications of Störmer's theory to aurorae, cosmic rays and Van Allen radiation belt particles are recalled in an historical perspective. In this paper, we expand the Störmer theory in order to take into account the effects produced by an additional uniform and stationary interplanetary magnetic field (IMF) whose orientation is parallel or antiparallel to the magnetic moment of the dipole. A new expression is derived for the Störmer potential taking into account the additional IMF component. It is shown how Störmer's allowed and forbidden zones are influenced by the implementation of a northward or a southward IMF, and how a southward turning of the IMF orientation makes it easier for Solar Energetic Particle and Galactic Cosmic Rays to enter into the inner part of the geomagnetic field along interconnected magnetic field lines.