In electrostatics, permeability is the measure of the ability of the material to allow the formation of magnetic lines of force or magnetic field within. It speaks on the ability of magnetization that material possesses for the applied magnetic field. It is denoted by the Greek alphabet μ.
The permeability of free space can be seen in an expression of a magnetic field of a long straight wire. The magnetic field B is produced by a long, straight conductor carrying by current I, at a distance r from the axis of the conductor, has magnitude B given by
B = μoI/2pir
In the equation above, μo is a constant called the permeability of vacuum. In SI units, the units of μo are (T. m/A). Its numerical value, which is related to the definition of the unit of current, is defined to be exactly 4pi x 10-7 (μ0 = 4𝝅×10-7 H/m, It is a scalar quantity). Kindly note that T. m/A means tesla metre per ampere. Also, 1 T. m/A is equal to 1 N/A2.
Also, the permeability of a material is defined by the relation μ = B/H, where B is the flux density and H is the magnetic field intensity. Μ, which is the ration of B/H, has dimensions; its unit is henry per meter (Hm-1)
Derivation of Relative Permeability
In General, B = μo(H + M). M is the magnetic moment
μ = B/H, therefore, B = μH
μH = μo(H + M)
μ/ μo = 1 + M/H
the ratio μ/ μo is called the relative permeability.
Lastly, magnetic permeability plays an important role in classifying the magnetization property of a material. The material is said to be diamagnetic if its magnetic permeability is less than μ0. Similarly, the material is said to be paramagnetic if its magnetic permeability is greater than μ0.
Read: Note on magnetic field