The electrostatic force can be given by:
Fe=14πε0q2r2
So, permittivity is:
So, ε0=q24πr2Fe
So, dimensions : ε0=[Q2][L2][MLT−2]
The dimensions of the permittivity ε is =[M−1L−3T2Q2]
The magnetic force can be given by:
Fm=μ04πqm1qm2r2
So, permeability is:
So, μ0=qm1qm24πr2Fm
The dimensions of the permeability μ is =[M1L1Q−2]
So, the ratio of the two dimensions is:
με=[M1L1Q−2][M−1L−3T2Q2]
⇒M2L4T−2Q−4
The dimension of the resistance is R=[ML2T−1Q−2]
comparing the dimension with the dimesion of resistance:
∴με=[R2]