Could we maybe add some numbers here? Like R=0.1 cm and Q=5*10^-7 C? Could do this as a charged balloon or something.

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.

• 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.

• 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