24.1: Electric Potential Energy
When an electric field accelerates a free positive charge q, it is given kinetic energy. The process is analogous to an object accelerated by a gravitational field as if the charge were going down an electrical hill where its electric potential energy is converted into kinetic energy. Of course, the sources of the forces are very different. The work done on a charge q by the electric field in this process helps to develop a definition of electric potential energy.
The electrostatic or Coulomb force is conservative, which means that the work done on q is independent of the path taken. This is exactly analogous to the gravitational force. When a force is conservative, it is possible to define the potential energy associated with the force. It is usually easier to work with the potential energy because it depends only on position than to calculate the work directly.
When a conservative force does negative work, the system gains potential energy. But when a conservative force does positive work, the system loses potential energy. For conservative forces, the change in potential energy is compensated by the change in the kinetic energy such that the total energy of the system remains constant.
For the system of like charges, the potential energy of the system decreases when charges move away from each other. On the other hand, for the system of opposite charges, the potential energy of the system decreases when charges move toward each other.
