In some of the questions in electrostatics, I came across 2 terms namely neutral equilibrium and stable equilibrium. Is there a difference between these 2?
There is a third class as well -- metastable equilibrium points. Suppose a system is very close to but not at some equilibrium point. The equilibrium point is Stable if forces act on the system to move it toward the equilibrium point Metastable (or unstable) if forces act on the system to move away from the equilibrium point Neutral if no dispersive or restoring forces act on the system. For example, a broomstick held by the end of the handle has two equilibrium points in a gravity field. The business end pointing along the gravity force vector (i.e., straight down) is a stable equilibrium point, while straight up is a metastable equilibrium point.
In a stable equilibrium, a slight change will lead to the system returning to its prior state. For instance, if you strectch a spring slightly, it will oscillate back to its still state. In a neutral equilibrium, a slight change won't necessarily lead to the system returning to the prior state, but it won't begin to diverge, either. Say, a sphere on a table. Push it slightly, and it will roll a bit and settle on another spot on the table. The disturbance affected the position, but not the stability.
And unstable is, for example, a ball at the top of a hill. In its current position it is stable - but a slight push in any direction and it rolls downhill - diverging from the equilibrium point.
