Question

Is coulomb’s law the same as the coulomb’s inverse square law?

Answer 1

In order to solve this question, we should know that here coulomb’s law is the law that governs the force between two static charges and coulomb’s inverse square law is the distance dependent laws, here we will discuss coulomb’s law of electrostatics and will figure out whether two laws are same or not.

Complete step by step answer:
In electrostatics, the force between two static charges was first formulated by Scientist Charles Coulomb. It states that if two charges having magnitudes of charge are ${q_1},{q_2}$ and they are separated by a distance of $r$ then electrostatic force between these two charges F is calculated as
$F = k\dfrac{{{q_1}{q_2}}}{{{r^2}}}$
where, $k = \dfrac{1}{{4\pi { \in _o}}}$ a proportionality constant having fixed value of $k = 9 \times {10^9}N$ and ${ \in _o}$ is known as permittivity of free space.

Coulomb’s inverse square law is simply states that force between two charges depends upon the square of distance between them inversely which can be written mathematically as $F \propto \dfrac{1}{{{r^2}}}$ and we see that, coulomb’s law of electrostatics is also similar to inverse square law $F = k\dfrac{{{q_1}{q_2}}}{{{r^2}}}$ so, In physics these two laws are not different but same.

Hence, yes coulomb’s law is the same as coulomb's inverse square law.

Note: It should be remembered that coulomb's inverse square law is the general law which governs almost all fundamental forces between two bodies which depends upon distance between the bodies and inversely square of the distance such as gravitational force, magnetism force, these all forces are inverse square law dependent.