A circular copper ring of radius r, placed in vacuum, has a charge q on it. Find out the electric fields at the centre of the ring.

Explanation

The charge q would be uniformly distributed along the circumference of the circular ring. So, the linear density of charge along the ring.
`lamda=q/(2pir)`
The electric field at the centre of the ring due to the charge on a small element of the ring would exactly be cancelled due to the charge on the diametrically opposite small element.
The whole ring is effectively an assembly of a large number of such diametrlcally opposite pairs of elements. As a result, the resultant electric field at the centre would be zero.