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184_notes:examples:week2_electric_potential_positive_point [2017/08/28 21:27] – [Example: Electric Potential from a Positive Point Charge] tallpaul | 184_notes:examples:week2_electric_potential_positive_point [2018/05/17 16:48] (current) – curdemma | ||
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===== Example: Electric Potential from a Positively Charged Balloon ===== | ===== Example: 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 at a point $P$, which is a distance $R=50 \text{ cm}$ from the center | + | Suppose we have a positively charged balloon with total charge $Q=5.0\cdot 10^{-9} \text{ C}$. What is the electric potential |
- | {{ 184_notes: | + | |
===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 | + | * 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}, | ||
- | ===Lacking=== | + | ===Representations=== |
- | * The electric potential at $P$. | + | <WRAP TIP> |
+ | === Assumption === | ||
+ | We assume | ||
+ | </ | ||
- | ===Approximations & Assumptions=== | + | [{{ 184_notes: |
- | * The electric potential at $P$ is due entirely to the balloon. | + | |
- | * $P$ lies outside of the balloon. | + | |
- | * The balloon' | + | |
- | * The electric potential infinitely far away from the balloon is $0 \text{ V}$. | + | |
- | ===Representations=== | + | ===Goal=== |
- | * The electric potential | + | * Find the electric potential |
====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 | ||
\begin{align*} | \begin{align*} |