A circular ring of charge of radius b has a total charge q uniformly distributed around it. What is the magnitude of the electric field at the center of the ring?

Zero.

Explanation:

First we divide the ring into infinitely small elements, Now considering one of those small elements. The electric field due to this element of charge is cancelled by another small element of charge situated at dramatically opposite side of the ring.

In this way the fields due to all small elements of the ring are cancelled by each other.

Thus the electric field magnitude at the center of the ring will be Zero.