Easy# Charged Disk: Limit as Diameter Tends to Infinity

EANDM-3N9AFS

The expression for the field at a distance $d$ along the center line perpendicular to a disk of radius $R$ with surface charge density $\sigma$ is given by:

$$ \vec E = \cfrac {\sigma}{2 \epsilon_0} \left[ 1 - \cfrac {d}{\sqrt {(d^2+ R^2)}} \right ] \widehat z$$

In the limit in which $R$ is much greater then $d$, which of the following expressions correctly describes the electric field due to the disk of charge?