# Why does electric potential increase with distance?

Dec 11, 2014

Actually, electric potential decreases as you move farther from a charge distribution.

First, think about more familiar gravitational potential energy. If you take an object sitting on a table, and do work on it by lifting it away from the earth, you increase the gravitational potential energy.

In the same way, as you do work on a charge to move it closer to another charge of the same sign, you increase the electric potential energy. That's because like charges repel each other, so it takes more and more energy to move the charges together the closer you get.

It's important to remember that electric potential and electric potential energy are two different things. Electric potential is the amount of potential energy per unit charge. If you pick a distance $r$ from a point charge, ${q}_{1}$, the potential will be;

$V \left(r\right) = \frac{k {q}_{1}}{r}$

$k$ is Coulomb's constant. When you place a second charge, ${q}_{2}$, at $r$, the potential energy, $W$, will be;

$W = V \left(r\right) {q}_{2}$

So potential is the scaling factor for the potential energy. Therefore, it increases as you get closer to the charge source.