French engineer and physicist Charles de Coulomb made pioneering discoveries in electricity and magnetism. He offered new theories about the force found between electrical charges, demonstrating that an electrically charged body can exert a force of attraction or repulsion at a distance on another charged body.

In 1785, he coined a tangible relationship in mathematical form between two bodies that were electrically charged. The physicist developed an equation that explains the force that makes bodies attract or repel each other, which became known as “Coulomb’s Law” or “Coulomb’s Law of the Inverse Square”.

## What does Coulomb’s Law say?

The force of attraction and repulsion of loads can be calculated by Coulomb’s Law. (Source: Wikimedia/Svjo/Reproduction)Source: Wikimedia/Svjo/Reproduction

Coulomb’s law expresses the strength of the electrical interaction between two electrically charged and immobile particles, allowing the calculation of the electrical force of both attraction and repulsion exerted between two stationary and charged objects. In fact, only the nature of electrical charges can allow us to identify the nature of the force, while the law allows us to calculate the intensity.

According to the physicist, the magnitude of the electrostatic force of attraction or repulsion between two electrically charged bodies is directly proportional to the product of the charge of the charged bodies and inversely proportional to the square of the distance between the center of the charged bodies.

The space in which the force is exerted is called an electric field. By convention, the electric field moves away from the positive charge as it moves toward the negative charge. Thus, the electric field always changes from a positive charge to a negative charge. The electric field of two charges of the same sign opposes itself, that is, it is oriented in opposite directions, while that of two opposite charges attracts.

The strength of the electric field depends on the charge of the object producing it and the distance from the charged object. The following equation allows you to calculate the strength of the electric field exerted by a charged body.

## Coulomb’s Law Formula

Coulomb’s Law formula is used to calculate the electrical force between 2 charges from the combination of the electrostatic constant (K), whose value in vacuum is 9.10^{9} N.m²/C², by the 2 electrical charges (q_{1} e q_{2}) multiplied with each other and divided by the square of the distance between the charges, in meters (r).

The unit of measurement of electrical charges used in the International System of Units (SI) is the Coulomb (C), in honor of the physicist who carried out the important formulation for the studies of electricity. The mass and dimension charges of electrical charges are considered negligible in Coulomb’s Law.

In calculating the intensity of the electrical force, only the absolute values of the charges are considered, disregarding their negative or positive sign. According to Newton’s Third Law, the force exerted by the charges on each other is equal in magnitude, as they are in the same direction, but in opposite directions.

## Graph of Coulomb’s Law

The graph represents a force inversely proportional to distance, such as the Coulomb force between a point load and a linear one.Source: Wikimedia/Chanchocan/Reproduction

Coulomb’s Law formula states that the electrical force between 2 charged particles is inversely proportional to the square of the distance between them. Thus, when 2 electrical charges are at a distance “d” and change their position to half that distance (d/2), the electrical force between them will be quadrupled (4F). Likewise, if the distance between the two charges is doubled, the electrical force between them will be decreased by 4 times.

Coulomb’s Law can be expressed in the form of a graph of force versus distance, in which the smaller the space between charges, the greater the electrical force; while the greater the distance, the lesser the force exerted on the electric field.

## Coulomb’s Law Applications

Electrostatic painting process is one of the applications of the Law of Coulomb. (Source: Pixabay/Magnascan/Reproduction)Source: Pixabay/Magnascan/Reproduction

The Law of Coulomb it is applied in the operation of copying machines, printers and in the painting of vehicles. The electrostatic process is responsible for the fixation of colored materials and for hair standing on end when touching a Van de Graff generator.

In the case of the copier, the machine uses a selenium-coated aluminum drum, as the electrical conductivity increases with exposure to light. In the first step of the xerography process, a negative charge is induced under a thin layer of positively charged selenium.

The drum surface is then exposed to the image to be copied; thus, the positive charge is neutralized where the image is bright, but remains where the image is dark. In this way, the image is transferred to the cylinder.

Then a dry black powder, called toner, is sprayed with a negative charge, which will be caused by the positive areas of the drum. A blank piece of paper receives a higher positive charge than the drum, then pulls toner out of the drum, and finally the paper and toner pass through heated rollers that melt and permanently adhere to the toner on the drum.