Coulomb law: what is it, formula and examples

What is Coulomb's Law?

Coulomb's law is used in the area of ​​physics to calculate the electrical 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 electric 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 forms the basis of electrostatics:

"The magnitude of each of the electrical forces with which two point charges at rest interact is directly proportional to the product of the magnitude of both charges and inversely proportional to the square of the distance that separates them and has the direction of the line that connects them. The force is of repulsion if the charges are of the same sign, and of attraction if they are of the opposite sign ”.

This law is represented as follows:

• F = electric force of attraction or repulsion in Newtons (N). Equal charges repel and opposite charges attract. k = is the Coulomb constant or electric 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 electrical charges measured in Coulomb (C). r = distance that separates the loads 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 C ² / (N · m ²). It is extremely important to take into account the permittivity of the material.

The value of the Coulomb constant in the International Measurement System 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 q ₁ and q ₂ without considering the loads around it.

Coulomb was able to determine the properties of electrostatic force by developing a torsion balance as a study instrument, which consisted of a bar that hung 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 force of attraction or repel as the bar rotated.

Electrostatic force

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

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

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

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

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

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. Now, if we rub an inflated balloon with our hair, the balloon will be charged with negative energy and when we bring it closer to the Teflon tape, both repel each other because they have the same type of charge.

Also, 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 system.

It is worth mentioning that for small distances the forces of electric charges increase, and for large distances the forces of electric charges decrease, that is, it decreases as the charges move away from each other.

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 given that bodies can attract or repel.

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

The magnitude of the electrostatic force is proportional to the product of the magnitude of the charges q ₁ xq ₂. The electrostatic force at close range is very powerful.

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 seen in the image, a negative force has been obtained.

Illustrated example of how to apply Coulomb's law:

Example 2

We have a charge of 6 x 10 ^-6 C (q ₁) that is 2m away from a charge of -4 x 10 ^-6 C (q ₂). 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 ^-6 C (q ₁) and another charge of -8 x 10 ^-6 C (q ₂) 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 acting between two electrical charges 1 x 10 ^-6 C (q ₁) and another charge of 2.5 x 10 ^-6 C (q ₂), which are at rest and in vacuum at a distance 5 cm (remember to take the cm am following the International System of measurements).

Answer: F = 9 N.