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184_notes:examples:week5_gauss_ball [2021/06/07 13:51] – schram45 | 184_notes:examples:week5_gauss_ball [2021/06/07 13:55] – schram45 | ||
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* The " | * The " | ||
* $\vec{E}(\vec{r})$ | * $\vec{E}(\vec{r})$ | ||
- | |||
- | ===Approximations & Assumptions=== | ||
- | * The ball is a perfect sphere. | ||
- | * There are no other charges that affect our calculations. | ||
- | * The ball is not discharging. | ||
- | * The ball is uniformly charged throughout its volume. | ||
- | * For the sake of representation, | ||
===Representations=== | ===Representations=== | ||
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* We represent the situation with the following diagram. The insulating case (part A) is shown on the left, and the conductor (part B) is on the right. | * We represent the situation with the following diagram. The insulating case (part A) is shown on the left, and the conductor (part B) is on the right. | ||
[{{ 184_notes: | [{{ 184_notes: | ||
+ | |||
+ | <WRAP TIP> | ||
+ | ===Assumptions=== | ||
+ | There are a few assumptions that can be made to simplify down our model before starting any calculations. | ||
+ | * There are no other charges that affect our calculations. | ||
+ | * The ball is not discharging. | ||
+ | * For the sake of representation, | ||
+ | </ | ||
+ | |||
====Solution (Part A)==== | ====Solution (Part A)==== | ||
A step-by-step approach to using Gauss' Law is shown in the [[184_notes: | A step-by-step approach to using Gauss' Law is shown in the [[184_notes: | ||
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<WRAP TIP> | <WRAP TIP> | ||
===Approximation=== | ===Approximation=== | ||
- | In order to take the electric field term out of the integral we must assume | + | In order to take the electric field term out of the integral we must approximate |
</ | </ | ||