Field Plots forming curvilinear squares

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1. The problem statement, all variables and given/known data

Drawing a field plot (using curvilinear squares) between a small sphere within a larger sphere, indicating lines of force and equipotentials.

I've been trying to find a software solution to draw the diagram perfectly, but haven't had any luck in finding one. I think it should be possible using Mathematica, however I wasn't success in finding assistance in the area.

2. Relevant equations



3. The attempt at a solution

I know how to draw the field plots by hand as it's not that trivial, although I really want to graph this using a computer so its perfect.

Does any one have any ideas?