Home exercise 3.3.3: Annular disk source

The field vanishes at the centre of the hole ($h=0$), although the potential there, ${\rho }_S(b-a)/(2{\epsilon }_0)$, is not zero: a zero field means a stationary potential, not a zero potential. For ${\rho }_S>0$, since $E_z>0$ for $h>0$ and, by symmetry, $E_z<0$ for $h<0$, the potential on the axis has its maximum at the centre of the hole, but only along the axis. In the plane of the ring the potential increases towards the charged ring, so the centre is a saddle point, consistent with the absence of extrema in a charge-free region.