[[184_notes:pc_potential|Return to Electric Potential]]
===== Example: Electric Potential from a Negatively Charged Balloon =====
Suppose we have a negatively 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 $R=20 \text{ m}$ from the center of the balloon?

===Facts===
  * The balloon has total charge $Q=-5.0\cdot 10^{-9} \text{ C}$.
  * The point $P$ is a distance $R=20 \text{ m}$ away from the center of the balloon.
  * The electric potential due to a point charge can be written as $$V = \frac{1}{4\pi\epsilon_0}\frac{q}{r},$$ where $q$ represents the charge and $r$ is the distance.

===Representations===
<WRAP TIP>
=== Assumption ===
We assume $P$ lies outside of the balloon. This is obvious, as $P$ is a distance $R=20 \text{ m}$ away from the center of the balloon.
</WRAP>
[{{ 184_notes:2_potential_positive_balloon.png?150 |Charged Balloon, and Point P}}]

===Goal===
  * Find the electric potential at $P$.

====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 a point very far from the balloon, so the balloon would "look" like a point charge from the perspective of an observation location that is $20 \text{ m}$ away.
</WRAP>

<WRAP TIP>
=== Assumption ===
The electric potential infinitely far away from the balloon is $0 \text{ V}$. Read [[184_notes:superposition#Superposition_of_Electric_Potential|here]] for why this is important.
</WRAP>

The electric potential at $P$ is given by
\begin{align*}
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{-5.0\cdot 10^{-9} \text{ C}}{20 \text{ m}} \\
  &= -2.2 \text{ V}
\end{align*}
Notice how the magnitude of charge on the balloon is the same as in the "positively charged balloon" [[184_notes:examples:Week2_electric_potential_positive_point|example]]. The reason the magnitude of the voltage is so much smaller, is because the distance is so much greater. [[184_notes:pc_potential#Potential_vs_Distance_Graphs|The closer you get to a point charge, the higher the magnitude of electric potential]].