Charles-Augustin de Coulomb and the units of charge

In the early eighteenth century and before, England had long been the scene for most of the important research and theorizing about the nature of electricity and magnetism. The focus shifted to France in the late eighteenth century. Scientists increasingly appreciated that scrupulous observation and exact measurement could provide a more realistic basis for understanding the physical world, as opposed to grandiose explanations involving vague notions such as effluvia and affinity of fluids.

Charles-Augustin de Coulomb played a central role in this new way of describing the basic forces of electrostatics and magnetism. He lived from 1736 to 1806, with many of his most active years coinciding with the French Revolution and its Napoleonic denouement. Notwithstanding, Coulomb managed to sidestep the attendant terrors and dislocations, spending the latter part of his life in seclusion and ill health while remaining highly productive. Despite setbacks, he continued his research into electrical and magnetic phenomena and formulated physical laws that described them.

Coulomb devised an instrument he called the torsion balance. It was capable of measuring very weak forces, physical, magnetic or electrical. This sensitive instrument provided insights into the nature and relations between key electrical parameters.

The distinguished thinker stated his Coulomb’s law in 1785. It provides that the electrostatic force between two charged objects is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This force exists along a straight line between the two objects. If the two charges are the same polarity, the objects repel one another. If the two charges are opposite in polarity, the objects attract one another.

Coulomb’s inverse-square law of electrostatic interaction resembles Newton’s inverse-square law of gravitation, with an important difference: As far as we know at this time, gravity is attractive only, never repulsive. Electrostatic interaction, in contrast, works both ways.

Why inverse-square? In both relations, the force, as it recedes, may be measured in an ever-expanding shell or sphere. A section of a sphere is a circle. The circumference of the circle is π times the diameter. To early theorists, this must have been self-evident.

The SI unit of electrostatic charge, like other units in the system, is named after a key researcher in the field. The coulomb is equal to the charge of 6.241 × 1,018 electrons. It is the charge transported by a uniform current of one ampere in one second. An ampere is the amount of current flowing in a conductor when 6.241 × 1,018 electrons pass a given point in one second.

It is also the amount of charge between the plates of a one-farad capacitor when the voltage between the plates is one volt. The water analogy is sometimes useful. Charge is equivalent to a quantity of water. Current is equivalent to the flow of a quantity of water per unit of time. Voltage is equivalent to pressure in a water system.