## Coulomb law

## What is Coulomb's Law?

Coulomb's law is used in the area of physics to calculate the electric force acting between two charges at rest.

From this law it is possible to predict what will be the electrostatic force of attraction or repulsion existing between two particles according to their electrical charge and the distance between them.

Coulomb's law owes its name to the French physicist Charles-Augustin de Coulomb, who in 1875 enunciated this law, and which constitutes the basis of electrostatics:

This law is represented as follows:

- F = electric force of attraction or repulsion in Newtons (N). Like charges repel and opposite charges attract.
- k = is the Coulomb constant or electrical constant of proportionality. The force varies according to the electrical permittivity (ε) of the medium, be it water, air, oil, vacuum, among others.
- q = value of the electric charges measured in Coulomb (C).
- r = distance that separates the charges and that is measured in meters (m).

It should be noted that the electrical permittivity of vacuum is constant, and one of the most widely used. It is calculated as follows: ε 0 = 8.8541878176x10-12 C2 / (N · m2). It is of utmost importance to take into account the permittivity of the material.

The value of the Coulomb constant in the International System of measurements is:

This law only takes into account the interaction between two point charges at the same time and only determines the force that exists between q1 and q2 without considering the charges around it.

Coulomb was able to determine the properties of the electrostatic force by developing a torsion balance as a study instrument, which consisted of a bar hanging on a fiber with the ability to twist and return to its initial position.

In this way, Coulomb could measure the force exerted on a point on the bar by placing several charged spheres at different distances in order to measure the attractive or repellent force as the bar rotated.

## Electrostatic force

Electric charge is a property of matter and is the cause of the phenomena associated with electricity.

Electrostatics is the branch of physics that studies the effects that are generated in bodies according to their electric charges in equilibrium.

The electric force (F) is proportional to the charges that come together and is inversely proportional to the distance between them. This force acts between the charges radially, that is, a line between the charges, hence it is a radial vector between the two charges.

Therefore, two charges of the same sign generate a positive force, for example: - ∙ - = + or + ∙ + = +. On the other hand, two charges with opposite signs generate a negative force, for example: - ∙ + = - or + ∙ - = -.

However, two charges with the same sign repel (+ + / - -), but two charges with different signs attract (+ - / - +).

Example: if you rub a Teflon tape with a glove, the glove is positively charged and the tape is negatively charged, so when they get closer they attract each other. Now, if we rub an inflated balloon with our hair, the balloon will be charged with negative energy and when it is brought closer to the Teflon tape, both repel each other because they have the same type of charge.

Likewise, this force depends on the electric charge and the distance between them, it is a fundamental principle of electrostatics, as well as a law applicable to charges at rest in a reference frame.

It should be mentioned that for small distances the forces of electric charges increase, and for large distances the forces of electric charges decrease, that is, they decrease as the charges move away from each other.

See also Electricity.

## Magnitude of force

Magnitude of the electromagnetic force is one that affects bodies that contain an electric charge, and that can lead to a physical or chemical transformation since bodies can attract or repel each other.

Therefore, the magnitude exerted on two electric charges is equal to the constant of the medium in which the electric charges are located by the quotient between the product of each of them and the distance that separates them squared.

The magnitude of the electrostatic force is proportional to the product of the magnitude of the charges q1 x q2. The electrostatic force at close range is very powerful.

See also Magnitude.

## Examples of Coulomb's Law

Below are different examples of exercises where Coulomb's Law should be applied.

### Example 1

We have two electric charges, one of + 3c and one of -2c, separated by a distance of 3m. To calculate the force that exists between both charges, it is necessary to multiply the constant K by the product of both charges. As can be seen in the image, a negative force has been obtained.

Illustrated example of how to apply Coulomb's law:

### Example 2

We have a 6 x 10-6C charge (q1) that is 2m away from a -4 x 10-6C charge (q2). So what is the magnitude of force between these two charges?

to. The coefficients are multiplied: 9 x 6 x 4 = 216.

b. The exponents are added algebraically: -6 and -6 = -12. Now -12 + 9 = -3.

Answer: F = 54 x 10-3 N.

### Examples of exercises

1. We have a charge of 3 x 10-6C (q1) and another charge of -8 x 10-6C (q2) at a distance of 2 m. What is the magnitude of the attractive force that exists between the two?

Answer: F = 54 X 10-3 N.

2. Determine the force that acts between two electric charges 1 x 10-6C (q1) and another charge of 2.5 x 10-6C (q2), which are at rest and in vacuum at a distance of 5 cm ( Remember to bring the cm to m following the International System of measurements).

Answer: F = 9 N.

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