Earnshaw’s theorem applies to electrostatic fields (ie, from non-moving charges) as well as magnetic fields. I think electrostatics are a bit easier to visualiz

Earnshaw’s theorem applies to electrostatic fields (ie, from non-moving charges) as well as magnetic fields. I think electrostatics are a bit easier to visualize than magnetostatics. There’s also a good analogous physical situation. Imagine you have a rubber sheet stretched into a plane. The challenge is to create a local minimum in the sheet by pushing it up in places. If you push it up with a tube to try to create a bowl, instead you’ll get a flat circle on top of the tube. My freshman year physics professor had us play with a program that simulated kinetic physics for point charges. You could “glue” charges to a plane, and then release other charges to see how they would respond. The end of the assignment said “Try to create a cage that can hold a charged particle. If you do, you might be eligible for a prize.”