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184_notes:examples:week5_flux_cube_plane [2017/09/19 13:45] – [Example: Flux through a Cube on a Charged Plane] tallpaul | 184_notes:examples:week5_flux_cube_plane [2017/09/22 15:57] (current) – dmcpadden | ||
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+ | FIXME - this is more or a homework problem for them. So I'm not sure we want to use this one... | ||
=====Example: | =====Example: | ||
Suppose you have a plane of charge with a uniform surface charge density of $\sigma=-4\mu\text{C/ | Suppose you have a plane of charge with a uniform surface charge density of $\sigma=-4\mu\text{C/ | ||
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When we plug in values for $\sigma$, $l$, and $\epsilon_0$, | When we plug in values for $\sigma$, $l$, and $\epsilon_0$, | ||
- | Notice that in the [[184_notes: | + | Notice that in the [[184_notes: |
$$\Phi_{\text{cube}}=\frac{Q_{\text{enclosed}}}{\epsilon_0}=\frac{\sigma l^2}{\epsilon_0}$$ | $$\Phi_{\text{cube}}=\frac{Q_{\text{enclosed}}}{\epsilon_0}=\frac{\sigma l^2}{\epsilon_0}$$ | ||
This is the same result! An alternative question for this example could have been: What is the electric field due to a uniformly charged plane? If we were not given the electric field at the beginning, we could have used symmetry arguments and Gauss' Law to work backwards, starting with the charge enclosed, and then using the integral formula for electric flux to solve for the electric field. There are sometimes electric fields that we do not know off-hand, and Gauss' Law is often the best tool to find them. | This is the same result! An alternative question for this example could have been: What is the electric field due to a uniformly charged plane? If we were not given the electric field at the beginning, we could have used symmetry arguments and Gauss' Law to work backwards, starting with the charge enclosed, and then using the integral formula for electric flux to solve for the electric field. There are sometimes electric fields that we do not know off-hand, and Gauss' Law is often the best tool to find them. |