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The figure below shows a disk of radius $R$ with a uniform surface charge density $\sigma$. We are interested in the electric field at a distance $d$ along a perpendicular line from the center of the disk of charge. In order to set up the problem we first want to determine the magnitude of the electric field, $dE$, created by the infinitesimal element of area shown by the hatched area in the figure below.

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Which expression below correctly describes the magnitude $dE$ due to the hatched area on the surface of the disk?


$\cfrac{\sigma r dr}{4 \pi \epsilon_0 (r^2+d^2)}$


$\cfrac{\sigma r dr d\theta}{4 \pi \epsilon_0 (r^2+d^2)}$


$\cfrac{\sigma r dr d\theta}{4 \pi \epsilon_0 (r^2+d^2)^{3/2}}$


$\cfrac{\sigma r dr d\theta}{4 \pi \epsilon_0 (r^2+d^2)^{1/2}}$


$\cfrac{\sigma r dr d\theta}{4 \pi \epsilon_0 d^2}$

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