- Using mass(M) , length(L) ,time(T) and current (A) as fundamental quantities, the dimension of permeability is

(1)M^{-1}LTA.

(2)ML^{2}T^{-2}A^{-1}

(3)MLT^{-2}A^{-2}.

(4)MLT^{-1}A^{-1}

Let us consider Coulomb’s law : F = q^{2} /(4πε_{0}×r^{2}) ;

q is charge in Coulomb, r is distance in metre, F is force in Newton and ε_{0} is permeability.

dimenison of ε_{0} = dimension of q^{2}/(F×r^{2}) = [Coulomb]^{2} /[Newton× square metre]…(1)

dimension of Coulomb = dimension of (Current×Time) = [ A T ]

dimension of Newton = [ MLT^{-2}]

substitute the above in (1), we have

dimension of ε_{0} = [ A^{2}T^{2} ]/ [MLT^{-2} × L^{2}] = [ A^{2} M^{-1} L^{-3} T^{4} ]