Examples

Example: Electric Potential from a Positively Charged Balloon

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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

• 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 electric potential due to a point charge can be written as

• where $q$ represents the charge and $r$ is the distance.

Representations

Assumption

We assume $P$ lies outside of the balloon. We make this assumption because it was not specified, but this seems to make more sense than $P$ being inside the balloon. This also helps us draw the representation below, which can be used to bolster our approximation later on of the balloon as a point charge.

Charged Balloon, and Point P

Goal

• Find the electric potential at $P$.

Solution

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 “look” like a point charge from the perspective of an observation location that is little far away.

Assumption

The electric potential infinitely far away from the balloon is $0\text{~V}$. Read here for why this is important.

The electric potential at $P$ is given by