Both gravity and electric force satisfy an inverse square law, and thus, both forces satisfy the shell theorem. That is, in a uniformly massive (or uniformly charged) spherical shell, there is no net force on any massive (or charged) object at any location within the shell.

Is this a unique property of inverse square functions? Or are there other functions that obey this? I reckon that I’ll have to solve a differential equation of some sort (or perhaps an integral equation). My gut tells me that this is a unique property of inverse square functions (what sort of differential equation would be satisfied by inverse square functions and another class of functions?). I’ll be investigating this further soon.

School’s out; the fun begins.