Coulomb

Coulomb

History

Coulomb’s law

Applications

Electrolytic cells

Resources

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 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 × 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 × 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 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, p₁ × 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 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