Question

The speed of light in vaccum $\left(c\right)$, depends on two fundamental constants, the permeability of free space $\left({\mu }_0\right)$ and permittivity of free space $\left({ϵ}_0\right)$. The speed of light is given by $c=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}$. The units of ${ϵ}_0$ are ${\text{N}}^{-1}{\text{C}}^2{\text{m}}^{-2}$. The units for ${\mu }_0$ are

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

Answer 1

The correct option is B ${\text{kg m C}}^{-2}$

Given relation is $c=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}$
$\Rightarrow {\mu }_0=\frac{1}{{ϵ}_0{c}^2}$
$\therefore$ units of ${\mu }_0=\frac{1}{\text{units of}{ϵ}_0{c}^2}$
$\Rightarrow \frac{1}{\left({\text{N}}^{-1}{\text{C}}^2{\text{m}}^{-2}\right)({\text{ms}}^{-1}{)}^2}=\text{N}{s}^2{\text{C}}^{-2}$
$\Rightarrow \left({\text{kg m s}}^{-2}\right)s^2{\text{C}}^{-2}={\text{kg m C}}^{-2}$