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?

• The balloon has total charge $Q=5\cdot 10^{-9} \text{ C}$.
• 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 $$V = \frac{1}{4\pi\epsilon_0}\frac{q}{r},$$ where $q$ represents the charge and $r$ is the distance.

• Find the electric potential at $P$.

• The balloon's electric field outside the balloon acts like a point charge centered at the center of mass of the balloon.
• 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

$$\begin{align*} V &= \frac{1}{4\pi\epsilon_0}\frac{q}{r} \\ &= \frac{1}{4\pi\cdot 8.85\cdot 10^{-12} \frac{\text{C}}{\text{Vm}}}\frac{5\cdot 10^{-9} \text{ C}}{0.5 \text{ m}} \\ &= 90 \text{ V} \end{align*}$$