Is it possible to have a hollow sphere with a continuous north pole on the outside and a continuous south pole on the inside?
Unfortunately, such an interesting construction is theoretically impossible. Several different mathematical models can be used to solve this problem, but for purposes of simplicity, an analogy with an often-stated problem with concentric charged conducting spheres will be used instead.
The electric field anywhere outside a charged conducting sphere is shown to be exactly equal to that produced by a point charge of equal total charge located at the center of the sphere. The field from a second sphere is likewise equal to that produced by a point charge located at its center. If the two spheres are concentric, the law of superposition may be used to show that the total field at any point outside both spheres is equal to that produced by the algebraic sum of the two equivalent point charges of both spheres. When the charges are equal and opposite, the sum will be exactly zero.
This is always true at all points outside both spheres. A permanent magnet may be represented precisely by an appropriate density of hypothetical magnetic charges on its two pole faces. Since there are no actual free magnetic charges or magnetic monopoles involved, the charges are always equal and opposite. Therefore, an equivalent result will be determined as for the electric example: the magnetic field outside the hollow magnetic shell will be zero everywhere.
Scott Wilber, President, ComScire - Quantum World Corporation
'As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.'