What is the potential energy on q due to this uniformly charged circular ring of radius r? (Point q is at the centre of the circle)

Potential at the centre due to circular ring of radius r and having uniform charge Q is KQ / r .

Point charge q is located at the centre of the ring.

Thus, potential energy of the system = charge q x potential

                             =  q x KQ / r

                             =  KQq / r .

Steps and Understanding :
1) We will find Electric Potential by writing V = K(q) / d 
where q is charge contained in ring. 
d - distance of charge from point .
k = 1/4π£° 
where £° is permitivity in vacuum. 

2) We will find Electric Field by 
E = -dV/dx