# Coulomb

# Coulomb

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

## History

By the early 1700s, Isaac Newton’s law of gravitational force had been widely accepted by the scientific community, which realized the vast array of problems to which it could be applied. During the period 1760– 1780, scientists began to search for a comparable law that would describe the force between two electrically charged bodies. Many assumed that such a law would follow the general lines of the gravitational law, namely that the force would vary directly with the magnitude of the charges and inversely as the distance between them.

The first experiments in this field were conducted by the Swiss mathematician Daniel Bernoulli around 1760. Bernoulli’s experiments were apparently among the earliest quantitative studies in the field of electricity, and they aroused little interest among other scientists. A decade later, however, two early English chemists, Joseph Priestley and Henry Cavendish, carried out experiments similar to those of Bernoulli and obtained qualitative support for a gravitation-like relationship for electrical charges.

Conclusive work on this subject was completed by Coulomb in 1785. The French physicist designed an ingenious apparatus for measuring the relatively modest force that exists between two charged bodies. The apparatus is known as a torsion balance. The torsion balance consists of a non-conducting horizontal bar suspended by a thin fiber of metal or silk. Two small spheres are attached to opposite ends of the bar and given an electrical charge. A third ball is then placed adjacent to the ball at one end of the horizontal rod and given a charge identical to those on the rod.

In this arrangement, a force of repulsion develops between the two adjacent balls. 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 that produced the distortion.

## Coulomb’s law

From this experiment, Coulomb was able to write a mathematical expression for the electrostatic force between two charged bodies carrying charges of q_{1} and q_{2} placed at a distance of r from each other. That mathematical expression was, indeed, comparable to the gravitation law. That is, the force between the two bodies is proportional to the product of their charges (q_{1} × q_{2} ) and inversely proportional to the square of the distance between them (1/r^{2}). Introducing a proportionality constant of k, Coulomb’s law can be written as: q_{1} × q_{2} F = kr^{2}, What this law says is that the force between two charged bodies drops off rapidly as they are separated from each other. When the distance between them is doubled, the force is reduced to one-fourth of its original value. When the distance is tripled, the force is reduced to one-ninth.

Coulomb’s law applies whether the two bodies in question have similar or opposite charges. The only difference is one of sign. If a positive value of F is taken as a force of attraction, then a negative < value of F represents a force of repulsion.

Given the close relationship between magnetism and electricity, it is hardly surprising that Coulomb discovered a similar law for magnetic force a few years later. The law of magnetic force is also an inverse square law. Specifically, p_{1} × p_{2} F = kr^{2}, where p_{1} and p_{2} are the strengths of the magnetic poles, r is the distance between them, and k is a proportionality constant.

## Applications

Coulomb’s law is fundamental to any study of electrical phenomena. It is also important in

### KEY TERMS

**Electrolytic cell—** An electrochemical cell in which an electrical current is used to bring about a chemical change.

**Inverse square law—** A scientific law that describes any situation in which a force decreases as the square of the distance between any two objects.

**Magnetic pole—** Either of the two regions within a magnetic object where the magnetic force appears to be concentrated.

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

**Qualitative—** Any measurement in which numerical values are not considered.

**Quantitative—** Any type of measurement that involves a mathematical measurement.

**Torsion—** A twisting force.

understanding many chemical phenomena. For example, an atom is, in one respect, nothing other than a collection of electrical charges, namely positively charged protons and negatively charged electrons. Coulombic forces exist among these particles. For example, a fundamental problem involved in a study of the atomic nucleus is explaining how the enormous electrostatic force of repulsion among protons is overcome in such a way as to produce a stable body.

Coulombic forces must be invoked also in explaining molecular and crystalline architecture. The four bonds formed by a carbon atom, for example, have a particular geometric arrangement because of the mutual force of repulsion among the four electron pairs that make up those bonds. In crystalline structures, one arrangement of ions is preferred over another because of the forces of repulsion and attraction among like-charged and oppositely-charged particles respectively.

## 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. Most people know that electrical appliances in their home operate on a certain number of “amps.” The ampere is defined as the flow of electrical charge per second of time. Thus, if one multiplies the number of amps times the number of seconds, 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 the British scientist Michael Faraday in about 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 of that cell. The Faraday relationship is fundamental to the practical operation of many kinds of electrolytic cells.

*See also* Electric charge.

## Resources

### BOOKS

Gilmor, C. Stewart. *Coulomb and the Evolution of Physics and Engineering in Eighteenth Century France.* Princeton, NJ: Princeton University Press, 1971.

Jones, Thomas P. *Electromechanics of Particles.* Cambridge, UK: Cambridge University Press, 2005.

Panofsky, Wolfgang K. H. and Melba Phillips. *Classical Electricity and Magnetism.* New York: Dover, 2005.

David E. Newton

# Coulomb

# Coulomb

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?

## History

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.

## Applications

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** ]

# Coulomb

# Coulomb

A coulomb (abbreviation: C) is the standard unit of charge in the **metric system** . It was named after the French physicist Charles A. de Coulomb (1736-1806) who formulated the law of electrical **force** that now carries his name.

## History

By the early 1700s, Sir Isaac Newton's law of gravitational force had been widely accepted by the scientific community, which realized the vast array of problems to which it could be applied. During the period 1760-1780, scientists began to search for a comparable law that would describe the force between two electrically charged bodies. Many assumed that such a law would follow the general lines of the gravitational law, namely that the force would vary directly with the magnitude of the charges and inversely as the **distance** between them.

The first experiments in this field were conducted by the Swiss mathematician Daniel Bernoulli around 1760. Bernoulli's experiments were apparently among the earliest quantitative studies in the field of **electricity** , and they aroused little interest among other scientists. A decade later, however, two early English chemists, Joseph Priestley and Henry Cavendish, carried out experiments similar to those of Bernoulli and obtained qualitative support for a gravitation-like relationship for electrical charges.

Conclusive work on this subject was completed by Coulomb in 1785. The French physicist designed an ingenious apparatus for measuring the relatively modest force that exists between two charged bodies. The apparatus is known as a torsion balance. The torsion balance consists of a non-conducting horizontal bar suspended by a thin fiber of **metal** or silk. Two small spheres are attached to opposite ends of the bar and given an electrical charge. A third ball is then placed adjacent to the ball at one end of the horizontal rod and given a charge identical to those on the rod.

In this arrangement, a force of repulsion develops between the two adjacent balls. 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 that produced the distortion.

## Coulomb's law

From this experiment, Coulomb was able to write a mathematical expression for the electrostatic force between two charged bodies carrying charges of q1 and q2 placed at a distance of r from each other. That mathematical expression was, indeed, comparable to the gravitation law. That is, the force between the two bodies is proportional to the product of their charges (q1 X q2) and inversely proportional to the square of the distance between them (1/r2). Introducing a proportionality constant of k, Coulomb's law can be written as: q1 X q2 F = kr2. What this law says is that the force between two charged bodies drops off rapidly as they are separated from each other. When the distance between them is doubled, the force is reduced to one-fourth of its original value. When the distance is tripled, the force is reduced to one-ninth.

Coulomb's law applies whether the two bodies in question have similar or opposite charges. The only difference is one of sign. If a positive value of F is taken as a force of attraction, then a **negative** value of F must be a force of repulsion.

Given the close relationship between **magnetism** and electricity, it is hardly surprising that Coulomb 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. In other words: p1 X p2 F = kr2 where p1 and p2 are the strengths of the magnetic poles, r is the distance between them, and k is a proportionality constant.

## Applications

Coulomb's law is absolutely fundamental, of course, to any student of electrical phenomena in **physics** . However, it is just as important in understanding and interpreting many kinds of chemical phenomena. For example, an atom is, in one respect, nothing other than a collection of electrical charges, positively charged protons, and negatively charged electrons. Coulombic forces exist among these particles. For example, a fundamental problem involved in a study of the atomic nucleus is explaining how the enormous electrostatic force of repulsion among protons is overcome in such a way as to produce a stable body.

Coulombic forces must be invoked also in explaining molecular and crystalline architecture. The four bonds formed by a **carbon** atom, for example, have a particular geometric arrangement because of the mutual force of repulsion among the four **electron** pairs that make up those bonds. In crystalline structures, one arrangement of ions is preferred over another because of the forces of repulsion and attraction among like-charged and oppositely-charged particles respectively.

## Electrolytic cells

The coulomb (as a unit) can be thought of in another way, as given by the following equation: 1 coulomb = 1 ampere X 1 second. The ampere (amp) is the metric unit used for the measurement of electrical current. Most people know that electrical appliances in their home operate on a certain number of "amps." The ampere is defined as the flow of electrical charge per second of **time** . Thus, if one multiplies the number of amps times the number of seconds, 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 the British scientist Michael Faraday in about 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** of that cell. The Faraday relationship is fundamental to the practical operation of many kinds of electrolytic cells.

See also Electric charge.

## Resources

### books

Brady, James E., and John R. Holum. *Fundamentals of Chemistry.* 2nd edition. New York: John Wiley and Sons, 1984.

Holton, Gerald, and Duane H. D. Roller. *Foundations of Modern Physical Science.* Reading, MA: Addison-Wesley Publishing Company, 1958.

Shamos, Morris H., ed. *Great Experiments in Physics.* New York: Holt, Rinehart and Winston, 1959.

Wilson, Jerry D. *Physics: Concepts and Applications.* 2nd edition. Lexington, MA: D. C. Heath and Company, 1981.

David E. Newton

## KEY TERMS

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .**Electrolytic cell**—An electrochemical cell in which an electrical current is used to bring about a chemical change.

**Inverse square law**—A scientific law that describes any situation in which a force decreases as the square of the distance between any two objects.

**Magnetic pole**—Either of the two regions within a magnetic object where the magnetic force appears to be concentrated.

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

**Qualitative**—Any measurement in which numerical values are not considered.

**Quantitative**—Any type of measurement that involves a mathematical measurement.

**Torsion**—A twisting force.

# coulomb

cou·lomb / ˈkoōˌläm; -ˌlōm/ (abbr.: C) • n. Physics the SI unit of electric charge, equal to the quantity of electricity conveyed in one second by a current of one ampere.

# coulomb

**coulomb ( koo-lom) n.** the SI unit of electric charge, equal to the quantity of electricity transferred by 1 ampere in 1 second. Symbol: C.

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