Question

State and explain Coulomb’s inverse square law in electricity.

Answer 1

Hint: When two electric charges are in vicinity of each other then it is noticed that like charges repel each other while the opposite charges attract each other. Coulomb gave the expression for this force which attracts or repels two charges. This law is known as the Coulomb’s law.

Detailed step by step solution:
Coulomb’s law gives the magnitude of the force by which two charges attract or repel each other. Consider that we have two point charges $q_1$ and $q_2$ which are separated from each other by a distance r. According to the Coulomb’s law, the force between these charges is
1. directly proportional to the product of the two charges.
$F\propto q_1{q}_2$
2. inversely proportional to the square of the distance between two given charges.
$F\propto {\displaystyle \frac{1}{r^2}}$
Combining these, we get
$$\begin{gathered} F\propto {\displaystyle \frac{q_1{q}_2}{r^2}} \\ F=K{\displaystyle \frac{q_1{q}_2}{r^2}} \end{gathered}$$
Here K is the constant of proportionality which is given as
${\displaystyle \frac{1}{4\pi {\in }_0}}=9\times {10}^{9}N{m}^2{C}^{-2}$
Therefore, the electrostatic force between two charges $q_1$ and $q_2$ is given by the Coulomb’s law by the following expression:
$F={\displaystyle \frac{1}{4\pi {\in }_0}}{\displaystyle \frac{q_1{q}_2}{r^2}}$
The ${\displaystyle \frac{1}{r^2}}$ dependence is known as the inverse square dependence. This means that the magnitude of the Coulomb’s force decreases with the square of the distance between two charges.

Note: 1. The Coulomb’s law is applicable for stationary charges. Also notice that we always talk about the point charges. This law does not take into consideration the size of the charge and is considered point-like. Also this force does not depend on the masses of the charges, only the charge on them.
2. The inverse square dependence is important because many laws of nature also show this ${\displaystyle \frac{1}{r^2}}$ dependence. For example, the gravitational law also has this dependence.
$F_G=G{\displaystyle \frac{m_1{m}_2}{r^2}}$
Also the Coulomb force is much stronger than gravitational force as two charges can attract or repel each other even in the gravitational field of earth.