The electric field \(\vec { E }\) created by a point charge q at a certain distance from it r in vacuum is given by \(\vec { E } = k _ { e } q \frac { \vec { r } } { r ^ { 3 } }\) , where \(k _ { e }\) is a constant.
Consider the charged ring of radius R with the linear charge density \(\frac { d q } { d l } \equiv \rho .\) Find the total magnitude of the electric field created by this ring at a distance d from its center along the axis orthogonal to it.
Consider the charged disk of radius R with surface charge density \(\frac { d q } { d A } \equiv \sigma\) Find the total magnitude of the electric field created by this disk at a distance d from its center along the axis orthogonal to it. Investigate the limit \(R \to \infty\)