A charged ring having radius $R$ and total charge $Q$ is lying in the x-y plane and centered at the origin. The expression for the electric field at $z \rightarrow \infty$ (in the z direction) is

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As $z \rightarrow \infty$, the ring of charge behaves like a point charge, and the electric field due to a point charge is given by $E = \frac{1}{4\pi\varepsilon_0} \frac{Q}{r^2}$, where $r$ is the distance from the charge. At very large distances ($z \rightarrow \infty$), the radius $R$ of the ring becomes negligible, so the distance $r$ can be approximated as $z$, leading to the formula $E_z = \frac{1}{4\pi\varepsilon_0} \frac{Q}{z^2}$.

A Charged Ring Having Radius RRR And Total Charge QQQ Is Lying in the X-Y Plane and Centered at the Is

A Charged Ring Having Radius $R$ And Total Charge $Q$ Is Lying in the X-Y Plane and Centered at the Is