Question

What is the $K$ in Coulomb's law?

Answer 1

1. If $q_1$ and $q_2$ are two charges, separated by a distance $r$, then according to Coulomb's law, the force $F$ is related by the following expression: $F\propto \frac{q_1{q}_2}{r^2}$
2. $F$ is proportional to the product of the charges and inversely proportional to square of the distance between them. Thus mathematical expression/formula from Coulomb's law is $F=K\frac{q_1{q}_2}{r^2}$, where $K$ is a proportionality constant
3. This proportionality constant $K$ is known as Coulomb's constant. The expression for this constant is $K=\frac{1}{4{\mathrm{\pi \epsilon }}_0}$. Here, ${\epsilon }_0$ is known as the permittivity of free space and has a value of $8.85\times {10}^{-12}{\mathrm{C}}^2·{\mathrm{N}}^{-1}{\mathrm{m}}^{-2}$.