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Example: Electric Potential from a Positive Point Charge
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 of mass of the balloon? A diagram below shows a rough sketch.
Facts
- The balloon has total charge $Q=5\cdot 10^{-7} \text{ C}$.
- The point $P$ is a distance $R=50 \text{ cm}$ away from the center of mass of the balloon.
Lacking
- The electric potential at $P$.
Approximations & Assumptions
- 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 $0 \text{ V}$.
Representations
- 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.
Solution
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^{-7} \text{ C}}{0.5 \text{ m}} \\ &\approx 9,000 \text{ V} \end{align*}