If you mean a perfectly radial magnetic field where the magnetic field lines start at the origin and spread out in all directions, than the answer is that such a field cannot exist. One of Maxwell's equations (the fundamental equations describing electromagnetic fields) states that the total magnetic field has no divergence. Conceptually, this means that you can never have perfectly radial magnetic fields.
As far as approximately radial magnetic fields, such as in a limited region around a magnetic pole, charged particles spiral around the magnetic fields lines and are repelled from the magnetic pole, for both cases of North pole and South pole. The earth's magnetic field is dipolar to a good approximation (at least right now it is), so that charged particles in the ionosphere are continually spiraling around the earth's magnetic field lines, bouncing back and forth between North and South poles.