Stability of 4 Charged Particles at Square Corners

[c299792458]

Homework Statement

Hi, I have a solution to this, but I am looking for a more elegant solution. If we are given 4 positively charged particles at the 4 corners of a square, is there a better proof for the stability of the central point of square for a 5th positively charged particle apart from (the clumsy way of) computing the 2nd partial derivatives of the U(x,y)...? Thanks!

Homework Equations

Coulomb's law

The Attempt at a Solution

computing the 2nd partial derivatives of the U(x,y)

 

[lanedance]

in essence it's the same but how about just calculating the force at a small displacement and show it always points back to the centre?