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184_notes:examples:week2_electric_potential_positive_point [2018/01/24 16:49] – tallpaul | 184_notes:examples:week2_electric_potential_positive_point [2018/01/24 17:42] – tallpaul | ||
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===== Electric Potential from a Positively Charged Balloon ===== | ===== Electric Potential from a Positively Charged Balloon ===== | ||
- | Suppose we have a positively charged balloon with total charge $Q=5\cdot 10^{-9} \text{ C}$. What is the electric potential (also called voltage) at a point $P$, which is a distance $R=50 \text{ cm}$ from the center of the balloon? | + | Suppose we have a positively charged balloon with total charge $Q=5.0\cdot 10^{-9} \text{ C}$. What is the electric potential (also called voltage) at a point $P$, which is a distance $R=50 \text{ cm}$ from the center of the balloon? |
===Facts=== | ===Facts=== | ||
- | * The balloon has total charge $Q=5\cdot 10^{-9} \text{ C}$. | + | * The balloon has total charge $Q=5.0\cdot 10^{-9} \text{ C}$. |
* The point $P$ is a distance $R=50 \text{ cm}$ away from the center of the balloon. | * The point $P$ is a distance $R=50 \text{ cm}$ away from the center of the balloon. | ||
* The electric potential due to a point charge can be written as $$V = \frac{1}{4\pi\epsilon_0}\frac{q}{r}, | * The electric potential due to a point charge can be written as $$V = \frac{1}{4\pi\epsilon_0}\frac{q}{r}, | ||
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===Goal=== | ===Goal=== | ||
* Find the electric potential at $P$. | * Find the electric potential at $P$. | ||
- | |||
- | ===Approximations & Assumptions=== | ||
- | * The balloon' | ||
- | * The electric potential infinitely far away from the balloon is $0 \text{ V}$. Read [[184_notes: | ||
- | |||
- | | ||
====Solution==== | ====Solution==== | ||
+ | <WRAP TIP> | ||
+ | === Approximation === | ||
+ | We approximate the balloon as a point charge. We do this because we have the tools to find the electric potential from a point charge. This seems like a reasonable approximation because the balloon is not too spread out, and we are interested in points outside the balloon. so the balloon might " | ||
+ | </ | ||
+ | |||
+ | <WRAP TIP> | ||
+ | === Assumption === | ||
+ | The electric potential infinitely far away from the balloon is $0 \text{ V}$. Read [184_notes: | ||
+ | </ | ||
The electric potential at $P$ is given by | The electric potential at $P$ is given by |