Question

The electrostatic force $F_e$ that an object of charge $Q$ exerts on another object of charge $q$ is given by Coulomb's law:
$F_e=\frac{1}{4\pi {ϵ}_0}\frac{Qq}{r^2}$
Where the charges of the two objects are $Q$ and $q$, are measured in units of coulombs $\left(C\right)$ and $r$ is the distance separating the two objects.
What are the units of the constant ${ϵ}_0$ ?

• A. $\text{kg}.m^3.s^{-2}.C^2$
• B. $\text{kg}.m^{-3}.s^2.C^{-2}$
• C. $\text{kg}.m.s^2.C^{-2}$
• D. $s^2.C^2.k{g}^{-1}.m^{-3}$

Answer 1

The correct option is D $s^2.C^2.k{g}^{-1}.m^{-3}$

Coulomb's Law can be rearranged to give ${ϵ}_0=\frac{1}{4\pi }\frac{Qq}{r^2{F}_e}$
Since, the units of both sides of the equation must be equal, the unit of ${ϵ}_0$ is $\frac{C^2}{m^2.kg.m.s^{-2}}$
​​​​​​​which can be simplified as $s^2.C^2.k{g}^{-1}.m^{-3}$