Lifting a ball stores gravitational potential energy, and far from Earth it is $U = -GMm/r$. Pushing two charges together, or pulling them apart, stores energy in the same way, with a formula of the same shape, built on Coulomb's law.
Why it works
The Coulomb force is conservative, like gravity: the work it does depends only on the start and the end. So there is a potential energy, and choosing $U = 0$ when the charges are far apart gives $$U = k\frac{q_1 q_2}{r}.$$ The signs of the charges stay in. Like charges repel: you must push to bring them together, and that work is stored, so $U > 0$ and it grows as they get closer. Unlike charges attract: they release energy as they come together, so $U < 0$, the same as gravity's $-GMm/r$.
Key idea
$U = k\dfrac{q_1q_2}{r}$, with signs, and $U = 0$ far apart. For several charges, add $U$ for every pair. With only electric forces acting, $K + U$ stays constant.
Worked examples
Worked example: Attracting charges
Find the potential energy of $+2.0\,\mu\text{C}$ and $-3.0\,\mu\text{C}$ charges $0.10\,\text{m}$ apart.
- $U = (8.99 \times 10^{9})\dfrac{(2.0 \times 10^{-6})(-3.0 \times 10^{-6})}{0.10} = -0.539\,\text{J}$.
- Negative: to pull them apart you must add $0.539\,\text{J}$.
Answer: $-0.539\,\text{J}$
Worked example: Released from rest
A $+3.0\,\mu\text{C}$ charge is fixed. A $2.0\,\text{g}$ ball with $+2.0\,\mu\text{C}$ is released $0.10\,\text{m}$ from it. How fast is the ball moving when it is very far away?
- At the start: $U = (8.99 \times 10^{9})\dfrac{(3.0 \times 10^{-6})(2.0 \times 10^{-6})}{0.10} = 0.539\,\text{J}$ and $K = 0$. Far away: $U = 0$.
- Energy is conserved: $\tfrac{1}{2}mv^2 = 0.539\,\text{J}$, so $v = \sqrt{\dfrac{2(0.539)}{0.0020}} = 23.2\,\text{m/s}$.
Answer: $23.2\,\text{m/s}$
Common mistake
Dropping the signs of the charges, so attracting charges seem to store positive energy. Keep the signs in $kq_1q_2/r$. Check with a picture: if the charges would fly together on their own, they lose potential energy as they approach, so $U$ must be negative and falling.
With three or more charges, add $kq_iq_j/r_{ij}$ for every pair: three charges make three pairs (1–2, 1–3 and 2–3). The total is the work it takes to bring the charges together from far apart, one at a time.