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

Explanation

` Radius =r `
` So, 2pir=circumference `
` Charge density=l, `
` total charge=2pirxxl `
` Electric potential =1/(4piepsilon_0)(2pirl)/sqrt(r^2+x^2) `
` 1/(2epsilon_0)-(rl)/(r^2+x^2)^(1/2) `
` So, Electric field =xcos theta `
` =(rl)/(2epsilon_0(R^2+x^2)^(1/2)).x/(r^2+x^2) `
` =(rlx)/(2epsilon_0(r^2+x^2)^(3/2))`