Electric Potential

Electric potential energy

Much like in mechanics, atoms can also have kinetic and potential energies. When an atom is held in place inside of an E-field, it has a certain potential energy - meaning, if it is let go, it will accelerate and gain some kinetic energy (converted from the potential energy the atom stored in its static state) as it moves away or towards the E-field source. Conservation is applied to electric charges just as it is to physical objects in mechanics!

Consider the following example. Two equal and oppositely charged plates create an E-field from left to right. Assume that atoms at points 1 and 2 are both positively charged and of the same magnitude. The atom at point 1 has more potential energy than that at point 2 because it is closer to the positively charged plate, meaning there is a stronger repulsive force between it and the plate. If both atoms are released, the atom at point 1 will accelerate at a much greater rate.

It is important to differentiate work done by the E-field vs. work done by an external force. The work done by the electric field is positive when the atom loses electric potential energy and gains kinetic energy. Conversely, the work done by an external force (think a hand pushing a positively charged atom forcefully towards another positively charged atom) is positive if the electric potential energy is increasing and negative if the kinetic energy increases. This concept can better be shown through the following equations:

Electric potential

It is important to understand the distinction between electric potential energy vs. electric potential, or voltage. While electric potential energy is in units of Joules, the units of voltage is Joules per Coulomb [J/C], or the volt [V]. The electric potential at some point P a distance r away from the source charge Q is calculated as

The electric potential difference between two points P1 and P2 can also be related to the E-field as

evaluated between P1 and P2.