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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:

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

...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?

A

$E = 0$

B

$E = \cfrac {\sigma R^2} {4 \epsilon_0 d^2}$

C

$E = \cfrac {\sigma } {2 \epsilon_0}$

D

$E = \cfrac {\sigma R} {2 \epsilon_0 d}$

E

$E = \cfrac {\sigma R^2} {2 \epsilon_0 d^2}$

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