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184_notes:examples:week5_flux_two_radii [2018/07/24 15:02] – curdemma | 184_notes:examples:week5_flux_two_radii [2021/06/04 00:47] (current) – schram45 | ||
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* $\Phi_e$ for each sphere | * $\Phi_e$ for each sphere | ||
* $\text{d}\vec{A}$ or $\vec{A}$, if necessary | * $\text{d}\vec{A}$ or $\vec{A}$, if necessary | ||
- | |||
- | ===Approximations & Assumptions=== | ||
- | * There are no other charges that contribute appreciably to the flux calculation. | ||
- | * There is no background electric field. | ||
- | * The electric fluxes through the spherical shells are due only to the point charge. | ||
===Representations=== | ===Representations=== | ||
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$$\vec{E}=\frac{1}{4\pi\epsilon_0}\frac{q}{r^2}\hat{r}$$ | $$\vec{E}=\frac{1}{4\pi\epsilon_0}\frac{q}{r^2}\hat{r}$$ | ||
* We represent the situation with the following diagram. Note that the circles are indeed spherical shells, not rings as they appear. | * We represent the situation with the following diagram. Note that the circles are indeed spherical shells, not rings as they appear. | ||
- | {{ 184_notes: | + | [{{ 184_notes: |
+ | |||
+ | <WRAP TIP> | ||
+ | ===Approximations & Assumptions=== | ||
+ | There are a few approximations and assumptions we should make in order to simplify our model. | ||
+ | * There are no other charges that contribute appreciably to the flux calculation. | ||
+ | * There is no background electric field. | ||
+ | * The electric fluxes through the spherical shells are due only to the point charge. | ||
+ | The first three assumptions ensure that there is nothing else contributing or affecting the flux through our spheres in the model. | ||
+ | * Perfect spheres: This will simplify our area vectors and allows us to use geometric equations for spheres in our calculations. | ||
+ | * Constant charge for the point charge: Ensures that the point charge is not charging or discharging with time. | ||
+ | </ | ||
====Solution==== | ====Solution==== | ||
Before we dive into calculations, | Before we dive into calculations, | ||
- | {{ 184_notes: | + | [{{ 184_notes: |
Since the shell is a fixed distance from the point charge, the electric field has constant magnitude on the shell. Since $\vec{E}$ is parallel to $\text{d}\vec{A}$ and has constant magnitude (on the shell), the dot product simplifies substantially: | Since the shell is a fixed distance from the point charge, the electric field has constant magnitude on the shell. Since $\vec{E}$ is parallel to $\text{d}\vec{A}$ and has constant magnitude (on the shell), the dot product simplifies substantially: |