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

\(\mu_{0}=k e^{a} m^{b} c^{c} h^{d}\)

\({\left[M L T^{-2} A^{-2}\right]=[A T]^{a}[M]^{b}\left[L T^{-1}\right]^{c}\left[M L^{2} T^{-1}\right]^{d}}\)

\(=\left[M^{b+d} L^{c+2 d} T^{a-c-d} A^{a}\right]\)

On comparingboth sides we get

\(a=-2 \quad \ldots(i)\)

\(b+d=1 \ldots(i i)\)

\(c+2 d=1 \ldots(i i i)\)

\(a-c-d=-2 \ldots(i v)\)

By equations \((i),(i i),(i i i)\) and \((i v)\) we get,

\(a=-2, b=0, c=-1, d=1\)

\(\left[\mu_{0}\right]=\left[\frac{h}{c e^{2}}\right]\)