A coulomb (abbreviation: C) is the standard unit of charge in the metric system. It was named after French physicist Charles A. Coulomb (1736–1806), who formulated the law of electrical force that now carries his name. (A physicist is one who studies the science of matter and energy.)

Coulomb's law concerns the force that exists between two charged particles. Suppose that two ping-pong balls are suspended in the air by threads at a distance of two inches from each other. Then suppose that both balls are given a positive electrical charge. Since both balls carry the same electrical charge, they will tend to repel—or push away from—each other. How large is this force of repulsion?


The period between 1760 and 1780 was one in which physicists were trying to answer that very question. They already had an important clue as to the answer. A century earlier, English physicist Isaac Newton (1642–1727) had discovered the law of gravity. Two objects attract each other, that law says, with a force that depends on the masses of the two bodies and the distance between them. The law is an inverse square law. That is, as the distance between two objects doubles (increases by 2), the force between them decreases by one-fourth (1 ÷ 2 2 ). As the distance between the objects triples (increases by 3), the force decreases by one-ninth (1 ÷ 3 2 ). Perhaps, physicists thought, a similar law might apply to electrical forces.

The first experiments in this field were conducted by Swiss mathematician Daniel Bernoulli (1700–1782) around 1760. Bernoulli's experiments were apparently among the earliest studies in the field of electricity that used careful measurements. Unfamiliar with such techniques, however, most scientists paid little attention to Bernoulli's results.

About a decade later, two early English chemists—Joseph Priestley (1733–1804) and Henry Cavendish (1731–1810)—carried out experiments similar to those of Bernoulli. Priestley and Cavendish concluded that electrical forces are indeed similar to gravitational forces. But they did not discover a concise mathematical formula like Newton's.

Words to Know

Electrolytic cell: Any cell in which an electrical current is used to bring about a chemical change.

Proportionality constant: A number that is introduced into a proportionality expression in order to make it into an equality.

Quantitative: Any type of measurement that involves a mathematical measurement.

Torsion: A twisting force.

The problem of electrical forces was finally solved by Coulomb in 1785. The French physicist designed an ingenious apparatus for measuring the small force that exists between two charged bodies. The apparatus is known as a torsion balance.

A torsion balance consists of two parts. One part is a horizontal bar made of a material that does not conduct electricity. Suspended from each end of the bar by means of a thin fiber of metal or silk is a ping-pong-like ball. Each of the two balls is given an electrical charge. Finally, a third ball is placed next to one of the balls hanging from the torsion balance. In this arrangement, a force of repulsion develops between the two adjacent balls (balls that are side by side). As they push away from each other, they cause the metal or silk fiber to twist. The amount of twist that develops in the fiber can be measured and can be used to calculate the force existing between the bodies.

Coulomb's law

The results of this experiment allowed Coulomb to write a mathematical equation for electrical force. The equation is similar to that for gravitational forces. Suppose that the charges on two bodies are represented by the letters q 1 and q 2 , and the distance between them by the letter r. Then the electrical force between the two is proportional to q 1 times q 2 (q 1 × q 2 ). It is also inversely proportional to the distance, or 1/r 2 .

The term inverse means that as one variable increases, the other decreases. As the distance between two charged particles increases, the force decreases. Furthermore, the change occurs in a square relationship. That is, as with gravitational forces, when the distances doubles (increases by 2), the force decreases by one-fourth (by ). When the distance triples (increases by 3), the force decreases by one-ninth (by ), and so on.

Electrical and magnetic forces are closely related to each other, so it is hardly surprising that Coulomb also discovered a similar law for magnetic force a few years later. The law of magnetic force says that it, too, is an inverse square law.


Coulomb's law is one of the basic laws of physics (the science of matter and energy). Anyone who studies electricity uses this principle over and over again. But Coulomb's law is used in other fields of science as well. One way to think of an atom, for example, is as a collection of electrical charges. Protons each carry one unit of positive electricity, and electrons carry one unit of negative electricity. (Neutrons carry no electrical charge and are, therefore, of no interest from an electrical standpoint.)

Therefore, chemists (who study atoms) have to work with Coulomb's law. How great is the force of repulsion among protons in an atomic nucleus? How great is the force between the protons and electrons in an atom? How great is the electrical force between two adjacent atoms? Chemical questions like these can all be answered by using Coulomb's law.

Another application of Coulomb's law is in the study of crystal structure. Crystals are made of charged particles called ions. Ions arrange themselves in any particular crystal (such as a crystal of sodium chloride, or table salt) so that electrical forces are balanced. By studying these forces, mineralogists can better understand the nature of specific crystal structures.

Electrolytic cells

The coulomb (as a unit) can be thought of in another way, as given by the following equation: 1 coulomb = 1 ampere × 1 second. The ampere (amp) is the metric unit used for the measurement of electrical current. (Electrical appliances in the home operate on a certain number of amps.) One amp is defined as the flow of electrical charge per second of time. Thus, by multiplying the number of amps by the number of seconds that elapse, the total electrical charge (number of coulombs) can be calculated.

This information is of significance in the field of electrochemistry because of a discovery made by British scientist Michael Faraday (1791–1867) around 1833. Faraday discovered that a given quantity of electrical charge passing through an electrolytic cell will cause a given amount of chemical change in that cell. For example, if one mole of electrons flows through a cell containing copper ions, one mole of copper will be deposited on the cathode or electrode of that cell. (A mole is a unit used to represent a certain number of particles, usually atoms or molecules.) The Faraday relationship is fundamental to the practical operation of many kinds of electrolytic cells.

[ See also Electric current ]

Also read article about Coulomb from Wikipedia

User Contributions:

Is the Coulomb Constant an absolute constant? What is the exact history behind it?
Erik Baalhuis
The Coulomb Constant is merely a conversion of units. We chose to define the speed of light and the meter, therefore making the Coulomb a secondary unit. The Coulomb Constant is introduced to make 1C = 1A / 1S.
This article is really enlightening and the approach of the author in bringing the explanation down to simple words makes the understanding very simple even to a notice.
Is Coulomb's law used today exactly as it was when Charles Coulomb himself came up with it?

Comment about this article, ask questions, or add new information about this topic: