sphere in a uniform magnetostatic field

[lheagy]

In geoana/geoana/em/static/sphere.py we should also include the solution for a permeable sphere in a uniform magnetostatic field. The solution for the magnetic field is in Ward and Hohmann (6.69). The derivation follows the conducting sphere in a uniform electrostatic field.

The implementation should include methods to compute:

• potential
• secondary magnetic field (Hs)
• total magnetic field
• secondary magnetic flux
• total magnetic flux

[lheagy]

A couple of minor suggestions based on @dccowan's implementation of the sphere in a uniform electrostatic field...

• the computation of vector distance is repeated quite a bit and this could be simplified ~replaced by the method geoana.spatial.distance that does this . e.g. we can replace this with geoana.spatial.distance~ see @jcapriot's comment below

• for the methods that compute fields / fluxes, I would suggest we have separate methods for computing and returning total, primary, and secondary current_density_total, current_density_primary, current_density_secondary. This makes them more discoverable and has the benefit of always providing outputs that are numpy arrays (whereas currently, you could get a numpy array or a list depending on how you call the function). This point is up for discussion and I would appreciate thoughts from @dccowan and @jcapriot

[jcapriot]

In my opinion there's a lot of redundant functions in that spatial module that are handled with simple operations... i.e. just call xyz - self.location instead of defining a function to just subtract two things... when calling for the distance, just use np.linalg.norm. My point is, there are already plenty of functions that already do these operations, and it's needless to wrap them.

[lheagy]

sounds good