Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision Next revision | Previous revision | ||
184_notes:examples:week2_electric_potential_positive_point [2017/08/28 21:24] – [Solution] tallpaul | 184_notes:examples:week2_electric_potential_positive_point [2018/05/17 16:48] (current) – curdemma | ||
---|---|---|---|
Line 1: | Line 1: | ||
- | ===== Example: Electric Potential from a Positive Point Charge | + | [[184_notes: |
- | Suppose we have a positively charged balloon with total charge $Q=5\cdot 10^{-7} \text{ C}$. What is the electric potential at a point $P$, which is a distance $R=50 \text{ cm}$ from the center | + | ===== Example: Electric Potential from a Positively Charged Balloon |
- | {{ 184_notes: | + | Suppose we have a positively charged balloon with total charge $Q=5.0\cdot 10^{-9} \text{ C}$. What is the electric potential |
===Facts=== | ===Facts=== | ||
- | * The balloon has total charge $Q=5\cdot 10^{-7} \text{ C}$. | + | * 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*} | ||
V &= \frac{1}{4\pi\epsilon_0}\frac{q}{r} \\ | V &= \frac{1}{4\pi\epsilon_0}\frac{q}{r} \\ | ||
- | &= \frac{1}{4\pi\cdot 8.85\cdot 10^{-12} \frac{\text{C}}{\text{Vm}}}\frac{5\cdot 10^{-7} \text{ C}}{0.5 \text{ m}} \\ | + | &= \frac{1}{4\pi\cdot 8.85\cdot 10^{-12} \frac{\text{C}}{\text{Vm}}}\frac{5\cdot 10^{-9} \text{ C}}{0.5 \text{ m}} \\ |
- | &\approx 9,000 \text{ V} | + | &= 90 \text{ V} |
\end{align*} | \end{align*} |