Question

Define Coulomb’s law for electrostatic force between two charges. Also write its limitations. Give definition of unit charge using this law.

Answer 1

Coulomb’s Law:
Each electric charge affects its surroundings. In this way, the surroundings mutually interacts and forms a force between its charges, called the electric force. In 1785, on the basis of experiments, Coulomb gave a law related with the force produced by two point charges. This law is called Coulomb’s law. According to this law, “the force of interaction between two point charges is directly proportional to the product of charges and inversely proportional to the square of the distance between them.”
If the two point charges q₁ and q₂ are placed at r distance, then
F ∝ q₁q₂ ………….. (1)
and F ∝ \(\frac{1}{r^2}\) …………….. (2)
⇒ F ∝ \(\frac{q_{1} q_{2}}{r^{2}}\) ⇒ F = \(\frac{k q_{1} q_{2}}{r^{2}}\) …………….. (3)
Here, k is a proportionality constant and its value depends upon the nature of medium between the charges and the unit system.
For vacuum or air (in S.I. unit)

This means that if maintaining a distance of 1m between two bodies of same charge in vacuum or air. a force of 9 x 10⁹ N acts between them. Then, the charge on each quantity is equal to one Coulomb. For a medium other than vacuum,

Vector Representation of Coulomb’s Law
Since force is a vector quantity. Thus, it is useful to write Coulomb’s law in vector form. For this, let us consider that two point charges q₁ and q₂ are placed at position vector \(\vec r_1\) and \(\vec r_2\) in vacuum. According to figure, the position vector of q₂ with respect to q₁ will be,

similarly, electric force on charge q₁ due to charge q₂.

So, we get to know that the force acting due to two charges are equal in magnitude but opposite in direction (whatever kind of charges they may). Thus, Coulomb’s law is in accordance with Newton’s third law of motion. Force is in the direction of the line joining the charges. Thus, constant electric force is central force.