You can make a Gaussian surface in the center, and the number of charges around it is zero, so the field strength is zero.

You can also take the infinitesimal dq on the ring, E=dq/s (dielectric constant). Take the opposite dq, and the results are the same in size and opposite in direction. However, there is such a pair of dqs anywhere in the ring, so it is zero.

I hope I can help you. D