 # Coulomb’s Law

##### What is Coulomb’s Law about?

Coulomb’s law (likewise called Coulomb’s inverse-square law) is a law of physics that specifies the amount of force in between two stationary, electrically charged particles (known as the electrostatic force). Coulomb’s law was discovered by Charles-Augustin de Coulomb in 1785. Hence the law and the associated formula were called after him.

##### Statement of Coulomb’s Law

According to Coulomb’s law, the force of attraction or repulsion between two charged bodies is directly proportional to the product of their charges and inversely proportional to the square of the distance in between them. It acts along the line joining up with the two charges thought about to be point charges.

##### Coulomb’s Law Mathematical Form

Let us suppose, Q1 and Q2 are the electrical charges of two objects. The distance between the charges is ‘r’, and the force of attraction or repulsion in between them is ‘F’. Then

F q1q2

Or, F1/r2

F = k q1q2/ r2 where k is proportionality constant and equals 1/4 π ε. Here, ε is the epsilon naught and it represents the permittivity of a vacuum. The value of k comes 9 × 109 Nm2/ C2 when we take the S.I unit of value of ε is 8.854 × 10-12 C2 N-1 m-2.

According to this theory, like charges repel each other and unlike charges attract each other. This suggests charges of the same sign will push each other with repulsive forces while charges with opposite signs will pull each other with attractive force.

Coulomb’s law equation gives a precise description of the force between two objects whenever the things act as point charges. A charged performing sphere connects with other charged things as though all of its charges lay at its center. While the charge is uniformly spread out throughout the surface of the sphere, the center of charge can be considered to be the center of the sphere.

The sphere acts as a point charge with its excess charge found at its center. Because Coulomb’s law applies to point charges, the distance r in the formula is the distance between the centers of charge for both objects (not the distance in between their closest surfaces).

##### Application of Coulomb’s Law
• To determine the distance and force between the two charges.
• To determine the force on one point due to the presence of several points.
##### Limitations of the Law

The law applies just for the point charges at rest.

• Coulomb’s Law can be just applied in those cases where the inverse square law is complied with.
• It is challenging to execute Coulomb’s law where charges remain in approximate shape since in such cases, we can not identify the distance in between the charges.
• The law can’t be utilized directly to determine the charge on the big planets or objects.