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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?

A

$\vec E = 0$

B

$\vec E = \cfrac{\sigma}{2 \epsilon_0} (1 - d) \widehat z$

C

$\vec E = \cfrac{\sigma}{2 \epsilon_0} \widehat z$

D

$\vec E = \cfrac{\sigma}{4 \epsilon_0} \widehat z$

E

$\vec E = \cfrac{\sigma \: d}{2 \epsilon_0} \widehat z$

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