If the charge of electron (e ), mass of electron (m ), speed of light in vacuum (c ) and Planck's constant (h ) are taken as fundamental quantities, then the permeability of vacuum ( ₀ ) can be expressed as

Step-by-step solution

We can expressed the permeability of vacuum, ( ₀ e^a m^b c^c h^d ) or ( ₀=k e^a m^b c^c h^d ) ...(i) Where, (k ) is a dimensional constant. As we know that, Dimension of ( aligned ₀ & = [ M L T ⁻² ~A ⁻² ], e & =[ AT ], m & =[ M ], c & = [ L T ⁻¹ ], h & = [ M L ^2 ~T ⁻¹ ], aligned ) and Putting the dimension of various physical quantities in Eq. (i), we get ( [ M L T ⁻² ~A ⁻² ]=k[ ~A ~T ]^a [ M ^b [ ~L ~T ⁻¹ ]^c ] [ M L ^2 ~T ⁻¹ ]^d ) ( [ M L T ⁻² ~A ⁻² ]=k[ M ]^ b+d [ ~L ]^ c+2 d [ ~T ]^ a-c-d [ ~A ]^a ) Comparing