Coulomb’s Law-Explanation Statement Formulas Principle Limitations

Coulomb’s Law-Explanation Statement Formulas Principle Limitations

Charles Augustin de Coulomb

Coulomb's law, or Coulomb's inverse-square law, is a law of physics describing the electrostatic interaction between electrically charged particles. The law was first published in 1785 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism. It is analogous to Isaac Newton's inverse-square law of universal gravitation. Coulomb's law can be used to derive Gauss's law, and reverse can be possible. The law has been tested heavily, and all observations have upheld the law's principle.

Coulomb's law statement:

1st law: 

The force is along the straight line joining them. If the two charges have the same sign, the electrostatic force between them is repulsive ; if they have different sign, the force between them is attractive

2nd law:

The magnitude of the electrostatic force of interaction between two point charges is directly proportional to the scalar multiplication of the magnitudes of charges and inversely proportional to the square of the distance between them

 

 FORMULAS OF COULOMBS LAW:

According to the Coulomb’s 2nd law,

Where,

   1. ‘F’ is the repulsion or attraction force between two charged bodies.
   2. ‘Q1’ and ‘Q2’ are the electrical charged of the bodies.
   3. ‘d’ is distance between the two charged particles.
   4. ‘k’ is a constant that depends on the medium in which charged bodies are presented. In S.I.          system, as well as M.K.S.A. system k=1/4πε. Hence, the above equation becomes.

The value of ε₀ = 8.854 X 10^-12 C²/Nm²

Hence, Coulomb’s law can be written for medium as,

Then, in air or vacuum ε_r = 1. Hence, Coulomb’s Law can be written for air medium as,

 The value of εr would change depends on the medium. The expression for relative permittivity ε_r is as follows,

PRINCIPLE OF COULOMBS LAW:

if we have two charged bodies one is positively charged and one is negatively charged, then they will attract each other if they are kept at a certain distance from each other. Now if we increase the charge of one body keeping other unchanged, the attraction force is obviously increased. Similarly if we increase the charge of second body keeping first one unchanged, the attraction force between them is again increased. Hence, force between the charge bodies is proportional to the charge of either bodies or both.

Now, by keeping their charge fixed at Q₁ and Q₂ if you bring them nearer to each other the force between them increases and if you take them away from each other the force acting between them decreases. If the distance between the two charge bodies is d, it can be proved that the force acting on them is inversely proportional to d² .

 This development of force is not same for all mediums. As we discussed in the above formulas, εr would change for various medium. So, depends on the medium, creation of force can be varied.

LIMITATIONS OF COULOMB'S LAW:

1. Coulomb’s Law is valid, if the average number of solvent molecules between the two interesting charge particles should be large.
2. Coulomb’s Law is valid, if the point charges are at rest.
3. It is difficult to apply the Coulomb’s Law when the charges are in arbitrary shape. Hence, we cannot determine the value of distance‘d’ between the charges when they are in arbitrary shape.