Question

The unit of permittivity is :

• A. $C^2{N}^{-1}{m}^{-2}$
• B. $N{m}^2{C}^{-2}$
• C. $H{m}^{-1}$
• D. $N{C}^2{m}^{-2}$

Answer 1

The correct option is A $C^2{N}^{-1}{m}^{-2}$

$\text{Step 1: Finding formula using permitivity}{ϵ}_0$

By Coulomb's law, the force between two charges $F=\frac{q_1{q}_2}{4\pi {ϵ}_0{r}^2}$
$\therefore {ϵ}_0=\frac{q_1{q}_2}{4\pi F{r}^2}$

$\text{Step 2: Finding Units of permitivity using above formula}$

Substituting the SI unit of all quantities on RHS of equation $\left(1\right)$.

We get, the unit of permittivity $\left({ϵ}_0\right)=\frac{C.C}{N.m^2}=C^2{N}^{-1}{m}^{-2}$

Hence option $\left(A\right)$ is correct