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Electricity and Magnetism

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Field Due to a Charged Disk: Starting Point

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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.

Created for Albert.io. Copyright 2016. All rights reserved.

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

A

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

B

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

C

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

D

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

E

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