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${\mu }_0=4\pi \cdot 10^{-7}N/A^2$.

The unit of ${\mu }_0$ is $Newton/Amper{e}^2=N/A^2=kgm/s^{2}1/A^2$

${\epsilon }_0=\frac{1}{{\mu }_0{c}^2}$

$=8.854\cdot 10^{-12}F/m$.

The unit of ${\epsilon }_0$ is Farad/m: $F/m=As/V=A^2{s}^4/(kg{m}^2)$