A small element Δl is cut from a circular ring of radius R and λ coulomb charge per unit length. The net electric field at the centre of ring is

Electric field due to ring at centre before the element is removed = 0E'=electric field at the centre after the element is removed. E''=electric field at the centre due to the element only =λ.Δl4πε0R2Now,   E→=E→'+E→''⇒   0=E'+λ . Δl4πεR2∴     E'   =  λ . Δl4πε0 . R2