22.5: Coulomb's Law
Experiments with electric charges have shown that if two objects each have an electric charge, they exert an electric force on each other. The magnitude of the force is linearly proportional to the net charge on each object and inversely proportional to the square of the distance between them. The direction of the force vector is along the imaginary line joining the two objects and is dictated by the signs of the charges involved.
Newton's third law applies to the Coulomb force — the force on each charge is equal in magnitude and opposite in direction to the force experienced by the other.
Interestingly, the Coulomb force does not depend on the mass of the objects. It is quantitatively similar to the gravitational force, the difference being that the latter is always attractive.
It is important to note that the electric force is not constant; it is a function of the separation distance between the two charges. If either the test charge or the source charge (or both) move, the separating distance changes; hence, the force changes. An immediate consequence is that the direct application of Newton’s laws with this force can be mathematically tricky. It can usually be done, but more straightforward methods of calculating whatever physical quantity we are interested in are preferred.
The new constant in Coulomb's law is called the permittivity of free space or the permittivity of vacuum. It has a significant physical meaning, related to the speed of light in vacuum.