Q: Difference in result of Electric field at the centre of a charged disc of uniform charge density We know that , the electric field $E$ due to a charged disc of radius $R$ ,with uniform charge density $\sigma$ , at a distance $Z$ on from its centre its axis is given by the formula
$$E= \frac{\sigma}{2{\epsilon_0}}\left(1 - \frac{Z}{\sqrt{{R^2}+{Z^2}}}\right)$$
And at $Z=0$(at its centre) , electric field E is
$$E=\frac{\sigma}{2{\epsilon_0}}$$
I thought of a different approach of finding the electric field at the centre , by considering infinitismally thin coaxial rings , of uniform charge density $\sigma$ ,of thickness $dx$ at distances $x$ from the centre , and then integrating the function of electric field at their centre ,from $x=0$ to $x=R$.
As the electric field by uniformly charged ring at its centre is $0$ , the final integral of all such rings must be $0$ . Therefore , $E=0$ .
But why through this new approach ,the electric field is  not $E=\frac{\sigma}{2{\epsilon_0}}$ ? Why there's a difference in the result?
Please help me out , any help is appreciated .
