Question

Consider a circular ring of radius r, uniformly charged with linear charge density λ. Find the electric potential at a point on the axis at a distance x from the centre of the ring. Using this expression for the potential, find the electric field at this point.

Answer 1

Radius = r So, 2πr = Circumference

Answer 2

Given:
Radius of the ring = r
So, circumference = 2πr  
Charge density = λ,
Total charge, q = 2πr × λ
Distance of the point from the centre of the ring = x
Distance of the point from the surface of the ring, 

Due to symmetry at point P, vertical component of electric field vanishes.
So, net electric field = Ecosθ