Question

If electron charge e, electron mass m, speed of light in vacuum c and Planck's constant h are taken as fundamental constant h are taken as fundamental quantities, the permeability of vacuum ${\mu }_0$ can be expressed in units of

• A. $\left(\frac{m{c}^2}{h{e}^2}\right)$
• B. $\left(\frac{h}{m{e}^2}\right)$
• C. $\left(\frac{hc}{m{e}^2}\right)$
• D. $\left(\frac{h}{c{e}^2}\right)$

Answer 1

The correct option is D $\left(\frac{h}{c{e}^2}\right)$

The fine structure constant is defined as $\alpha =\frac{e^2}{4\pi {ϵ}_0\hslash c}$ and is dimensionless where $\hslash =\frac{h}{2\pi }$

$\therefore \alpha =\frac{e^{2}c}{4\pi {ϵ}_0\hslash c^2}=\frac{e^{2}c{ϵ}_0{\mu }_0}{4\pi {ϵ}_0\hslash }$ where $c=\frac{1}{\sqrt{{ϵ}_0{\mu }_0}}$

$\Rightarrow {\mu }_0=\frac{\hslash }{e^{2}c}$