Suppose we have an infinite set of positive and negative charges next to each other: $$... + - + - + - ...$$
I am wondering if this a position of equilibrium.
Intuitively I would say that it is a position of equilibrium since the negative charge on the left of $+$ repeal $+$ in the right direction as much as the $-$ on the right which repeal $+$ on the left. Moreover if I take one $+$ and get it off this infinite set then we will have the following position of equilibrium :
$$... + - + - - + ...$$ Thus the two $-$ are going to move onto each other.
I don't really know if what I am saying is false, if it's a good justification...
So is this infinite set a position of equilibrium and how to "prove" it ?