22.5:
Coulomb’s Law
Electrical experiments lead to a mathematical law that quantifies observations. Coulomb's law formulates the force of attraction or repulsion between two point charges.
Consider two electrically charged point masses, with charges q-1 and q-2. They experience the same magnitude of force, called the Coulomb force. It is directly proportional to the product q-1-q-2 and inversely proportional to the square of the distance between them. It acts along the imaginary line joining them.
In the SI units, the proportionality constant is approximately 8.988 times 109. For theoretical reasons, it is described via another constant, epsilon-naught, known as the permittivity of vacuum. Its value is 8.854 times 10-12 in SI.
If both the charges are positive, or both are negative, they experience equal and opposite force away from each other. If one charge is positive and the other is negative, the force is attractive and equal.
The inverse square nature of the force implies that it is effective only at small distances. Friction is an example of a Coulomb force.
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.
Suggested Reading
- OpenStax. (2019). University Physics Vol. 2. [Web version]. Retrieved from https://openstax.org/details/books/university-physics-volume-2; section 5.3; page 192.