The maximum electric field intensity on the axis of a uniformly charged ring of charge q and radius R will be :
14πε0q33R2
14πε02q3R2
14πε02q33R2
14πε03q22R2
E=kqx(R2+x2)3/2, for maximum E, dEdx=0
⇒kq(1)(R2+x2)3/2+-32kqx(R2+x2)5/2(2x)=0
⇒R2+x2=3x2⇒x2=R22
⇒Emax=kq(R/2)R2+R223/2=2kq33R2