Coulomb's law

Coulomb's law or Coulomb's inverse-square law is a low of physics used to quantify the amount of force between two stationary elctrically charged particles.

Electrostatic Force

Electrostatic force or Coulomb force is defined as the electric force between two charged bodies at rest. The quantity of electrostatic force between stationary charges is always described by Coulomb's law.

𝐹=14𝜋𝜀𝑒𝑄1𝑄2𝑟2𝑟=𝑘𝑒𝑄1𝑄2𝑟2𝑟

The direction of force is attractive if charges have opposite sign as above and is repulsive if charges have same sign as below. The electrostatic force always acts along a line connecting tht charges

The magnitude of electrostatic force is proportional to the magnitude of each charge and inversely proportional to the distance squared

𝐹=𝐹=14𝜋𝜀𝑒|𝑄1𝑄2|𝑟2=𝑘𝑒|𝑄1𝑄2|𝑟2

The unit of electric charge, 𝑄 in SI unit is Coulomb, 𝐶. The unit of electrostatic force, 𝐹 is 𝑁. The unit of distance, 𝑟 is 𝑚. Therefore the unit of permittivity, 𝜀 is 𝐶²/𝑁𝑚².

The vacuum permittivity, 𝜀₀ is equal to 8.85×10^-12𝐶²/𝑁𝑚²=8.85×10^-12𝐹𝑚^-1. The Coulomb's constant, 𝑘_𝑒 for vacuum, 1/4𝜋𝜀₀ is 9×10⁹𝑁𝑚²/𝐶²

The electric charge of an electron, 𝑒 is 1.602×10^-19𝐶. The electric charge quantity of an electron, 𝑄 is −𝑒, while the electric charge quantity of a proton, 𝑄 is +𝑒.

Electric Field

From Coulomb's law, a particle with electric charge, 𝑄₀ at position, 𝑥₀ exerts a force on a particle with electric charge, 𝑄₁ at position, 𝑥₁ can be expressed as 𝐹=14𝜋𝜀0𝑄0𝑄1(𝑥1−𝑥0)2𝑟 The effect of the source charged particles 𝑄₀ at position 𝑥₀ on charged particles, 𝑄₁ at position 𝑥₁can be expressed as 𝐹0,1𝑄1=14𝜋𝜀0𝑄0(𝑥1−𝑥0)2𝑟0,1 Since charged particles exerts electrostatic forces in all direction at all times, whether or not there is another charged particles around, the effect of the source charged particles at position, 𝑥 on charged particles, 𝑄 throughout space at all time can be expressed as 𝐸𝑥=𝐹𝑥𝑄=14𝜋𝜀0𝑄0(𝑥−𝑥0)2𝑟𝑥 This is the electric field which is equal to Electrostatic force per unit charge that a point charge 𝑞 of the same sign would exprerience at position 𝑥 due to the charged particles, 𝑄₀ of positive charge 𝑞₀ at position 𝑥₀. The unit of electric field is Newton/Coulomb. In other words, the electrostatic force that acts on any charge can be expressed as 𝐹=𝑞𝐸=14𝜋𝜀0𝑞0𝑟2𝑟 The direction of electric field due to a charged particle is only affected by the sign of charges. A positive charged particle generates a pointing outward electric field, while a negative charged particle generates a pointing inward electric field. The direction of electrostatic force acting on an charaged observed particle due to the electic field generated by a charged source particle depends on the signes of the two charged particles. However, a positively charged observed particle alway experences an electrostatic force which is along with the same direction of electric field, while a negatively charged observed particle particle alway experences an electrostatic force which is against the direction of electric field, i.e. in the opposite direction of electric field.

Source and Reference

https://www.youtube.com/watch?v=v57B_1ZBAho&list=PLZ6kagz8q0bvxaUKCe2RRvU_h7wtNNxxi&index=1