Introduction to Coulomb's Law

Relevance of the Topic

Coulomb's Law is one of the cornerstones of Physics, being intrinsically linked to the study of Electricity and Magnetism. This law describes the behavior of electric charges interacting with each other and is the basis for understanding phenomena such as electrostatic pressure, the force between electric currents, and the force acting on a charged particle in an electric field.

Contextualization

In the Physics curriculum, Coulomb's Law is often introduced after the study of the concept of electric charges, such as positive and negative charges, and the principles of electrification. This prior knowledge is essential for understanding Coulomb's Law, which quantifies the forces acting between these charges. The law is also closely associated with Newton's Law, allowing us to understand that electrostatic force follows the same principle of inertia: 'an object tends to remain in its state of motion until a force acts upon it.' This parallel contributes to a more unified view of the physical world.

Theoretical Development

Components

• Electric Charge: Coulomb's Law is defined in terms of the interaction between electric charges. Charges of the same sign repel each other, while charges of opposite signs attract each other. The measure of the amount of charge is the coulomb (C), where the charge of a proton is +1.602 x 10^-19 C and the charge of an electron is -1.602 x 10^-19 C.

• Distance between Charges: The electrostatic force, determined by Coulomb's Law, is inversely proportional to the square of the distance between the charges. The closer the charges are, the greater the force.

• Electric Constant: Represented by k, it is a property of the medium in which the charges are interacting. In a vacuum, the electric constant is 9 x 10^9 N.m^2/C^2.

Key Terms

• Electrostatic Force: Also known as Coulomb's force, it is the force that acts between two electric charges when they are at rest. It is directly proportional to the product of the charges and inversely proportional to the square of the distance.

  • Coulomb's Law: Enunciated by Charles Augustin de Coulomb, Coulomb's Law describes the electrostatic force between two point charges. Mathematically, it is expressed as F = k.q1.q2/r^2, where F is the force, q1 and q2 are the charges, r is the distance between them, and k is the electric constant.

Examples and Cases

• Force between two electrons in a vacuum: Considering two electrons in a vacuum, each with a charge of -1.602 x 10^-19 C and separated by a distance of 1 x 10^-10 m, we can calculate the electrostatic force using Coulomb's Law.

  • In a vacuum, k = 9 x 10^9 N.m^2/C^2. Thus, the force between them will be F = 9 x 10^9 x 1.602 x 10^-19 x 1.602 x 10^-19 / (1 x 10^-10)^2 = 2.3 x 10^-8 N. Note that the force is repulsive, as expected for two electrons with charges of the same sign.

• Force between a proton and an electron in a medium with dielectric constant ε: When considering a proton with a charge of +1.602 x 10^-19 C and an electron with a charge of -1.602 x 10^-19 C separated by a distance of 1 x 10^-10 m in a medium with a dielectric constant ε = 4ε₀, where ε₀ is the permittivity of vacuum, the force will be F = k.q1.q2/ε.r². Note that the force is reduced by the dielectric constant allowing for smaller forces to act at the same distance.

The applications of Coulomb's Law extend beyond the examples discussed here, including the interaction between particles in electric fields such as that of a capacitor and the determination of charge distribution in electrified bodies.

Detailed Summary

Key Points

• Approximation of point charges: Although real electric charges may not be point-like, Coulomb's Law is applicable when the distances between the charges are much larger than their linear sizes, which is the case in most applications.

• Influence of distance: The electrostatic force between two charges is inversely proportional to the square of the distance between them, meaning that the closer the charges are, the greater the force.

• Nature of the force: The force between charges of the same sign (positive or negative) is repulsive, while between charges of opposite signs is attractive. This is a fundamental characteristic of electromagnetic interactions.

• Electric Constant: The electric constant, represented by k in Coulomb's Law, depends on the medium in which the charges are interacting. In a vacuum, k has a fixed value of 9 x 10^9 N.m^2/C^2.

Conclusions

• Interdependence of variables: Coulomb's Law demonstrates the interdependence between electrostatic force (F), charges (q1 and q2), and distance (r). Changing any of these variables will have a direct impact on the resulting force.

• Balance of forces: Coulomb's Law works in conjunction with other principles, such as Newton's Law, to form a complete understanding of the forces acting in the physical world.

Suggested Exercises

1. Force between two charges: Calculate the electrostatic force between two identical charges of 1 μC separated by a distance of 1 m in a vacuum.

2. Scale of forces: Compare the electrostatic force between two electrons at a distance of 1 m in a vacuum with the gravity exerted by an apple (mass of 0.1 kg) at a distance of 1 m. (Consider G = 6.67 * 10^-11 N.m^2/kg^2)

3. Force in a dielectric medium: Consider a proton and an electron separated by 1 nm in a dielectric medium with a dielectric constant ε = 3ε₀. Calculate the electrostatic force between them.