Suppose we have a negatively charged balloon with total charge $Q=-5.0\cdot 10^{-9} \text{ C}$. What is the electric potential at a point $P$, which is a distance $R=20 \text{ m}$ from the center of mass of the balloon? A diagram below shows a rough sketch.

• 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 mass of the balloon.

• The electric potential at $P$.

• The electric potential at $P$ is due entirely to the balloon.
• $P$ lies outside of the balloon.
• 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 $0 \text{ V}$.

• The electric potential due to a point charge (to which we are approximating the balloon) can be written as $$V = \frac{1}{4\pi\epsilon_0}\frac{q}{r},$$ where $q$ represents our charge and $r$ is our distance.

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” example.