Past exam of the physics course of the year 4 of the natural sciences course of the University of Cambridge / 2015 / Paper 1 / Section A / A8

An element at $a(\cos \varphi ,\sin \varphi ,0)$ carries charge $dq={\lambda }_{0}a\sin \varphi d\varphi$. Its field at the origin points opposite its radial position. By Coulomb's law,ConsequentlyFor $q{\lambda }_0>0$ the particle starts along $-y$; for the opposite sign it starts along $+y$. Reflection symmetries make the $y$ axis invariant for motion released there from rest. The ring has zero net charge but a nonzero dipole moment, so zero total charge does not imply zero field at its centre.