NOTES
Suppose you made the spinning parabolic wire into a spinning parabolic bowl, and placed a pile of sand at one point on the bowl. The pile of sand would spread out due to the perpendicular force, to create a new equipotential surface, also parabolic. In fact, if you put sand or water in a spinning hemisphere, or a spinning cone you’d get a parabolic shape when the sand or water reached equilibrium - the equipotential shape is the nature shape for anything not strong enough to hold its own shape.