Imagine a sphere such that positive charge is evenly distributed throughout one hemisphere (not just on the surface) and equal negative charge is evenly distributed throughout the other hemisphere. Is there a simple or elegant way to map out the magnetic field inside/outside the sphere and predict the behavior of the field (magnitude, direction) at any arbitrary point inside/outside the sphere? P.S. Ignore the little plus sign outside the sphere, or better yet, pretend it's a test charge. Also, if you can't make heads or tails of how the sphere would work out, then let me know if you have any ideas how a spherical shell with analogous properties would behave.