You may be familiar with the concept of potential energy from your science class. Basically, if an object has the potential to do work, then we say it has potential energy. For example, say you are standing on your roof, holding a baseball. When you are holding the baseball, it has a certain amount of potential energy from gravity. If you were to drop the ball off the roof, that potential energy would be converted to kinetic energy, or the energy of motion.
Any conservative force has a potential energy associated with it. The coulomb force is conservative, so, you guessed it, we have electric potential energy.
Work is defined by a force multiplied by the distance the force is applied for. We know that the coulomb force is:
and since the distance the force acts over is r, we can multiply by r, and obtain:
Note the absolute value signs missing from the bottom equation. Force is a vector quantity, so the absolute value signs were needed, but because work is a scalar quantity, we definitely want the sign of our charges to tell us how the amount of electric potential energy is changing.
Now for the confusing part. What we just learned about was electric potential ENERGY. Now we will learn about electric potential. Although they are closely related, they are two completely separate quantities. (And you thought scientists were supposed to be creative.....) Don't let the names fool you. These are important physical concepts, and you should feel comfortable knowing which is which.
Electric potential is defined as work per unit charge. i.e.
alternately, we can write this as:
The units of electric potential are volts, named after Alessandro Volta. 1 volt is equivalent to 1 joule per coulomb.
Electric potential is still another quantity that obeys the principle of superposition. Because it is not a vector quantity, care must be taken to keep the sign of the charges correct when adding the potentials of more than one charge.
Although we will not cover this topic in any depth, you should know that regions where the electric potential has a constant value are known as equipotentials. These are most often represented by lines or surfaces.