Moderate# Charged Disk: Limit as Distance from Disk Tends to Infinity

EANDM-N9EBFS

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:

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

...where the direction $\widehat z$ is perpendicular to the plane of the disk.

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