What is the dimensional formula for permeability

This is magnetic permeability or simply permeability. It is ability of a medium to allow the formation of magnetic field. It varies from medium to medium and depends upon frequency of magnetic field, temperature and other parameters .Permeability is generally denoted by ‘μ’ . Talking about its dimensional formula first we should know that it is equal to ratio of intensity of magnetic field ( simply magnetic field ) to magnetising field ( i.e. the degree to which a magnetic field can magnetise a material).

μ = intensity of magnetic field (B)/Intensity of magnetising field (H)

As we know , unit of intensity of magnetic field is Tesla or Newton per Ampere metre (N/Am)

And unit of magnetising field is Ampere per metre (A / m).

So we can find by above formula that permeability has unit Newton per Ampere square

μ = Newton / Ampere square

Or μ = N/ A ²

By calculating their dimensions we will get the dimension of permeability to be

[M L T^{-2} I ^{-2}].