What-is-the-value-of-magnetic-field-within-a-hollow-sphere?
Answers
This is difficult, because just saying "the sphere is magnetic" isn't really enough information. There are lots of ways one could theoretically magnetize a sphere.
Magnetic materials work in something called "magnetic domains". Magnets of any variety always have a north and south pole (there's no such thing as a magnetic monopole). The way that these poles arrange themselves change their characteristics.
For example, suppose we oriented our surface so that all of the North poles were on the outside of the sphere, and all of the South poles are on the inside of the sphere. This would result in no net magnetic field inside the sphere due to Gauss's Law.
However, let's suppose in stead that we oriented the magnetic domains such that the north pole always pointed towards the "top" of the sphere. In this case, there will definitely be a magnetic field within the sphere (and it will be pointing towards the "bottom" of the sphere, though I don't know how it will vary in different parts of the interior).
One could always come up with various other complicated scenarios with the magnet domains breaking up into smaller domains and pointing in different direction. It's worth noting that the Hairy Ball Theorem shows we have to have at least one point where the magnetic field is at least not parallel to the surface.