Absolute Permeability and Relative Permeability

In Figure given below it is shown a bar of a magnetic material, say, iron placed in a uniform field of strength H N/Wb. Suppose, a flux density of B Wb/m² is developed in the rod.

Then, the absolute permeability of the material of the rod is defined as
μ = B/H henry/metre or B = μH = μ₀μ_r H Wb/m² …………………..(i)

When H is established in air (or vacuum), then corresponding flux density developed in air is
B₀ = μ₀H

Now, when iron rod is placed in the field, it gets magnetised by induction. If induced pole strength in the rod is m Wb, then a flux of mWb emanates from its N-pole, re-enters its S-pole and continues from S to N-pole within the magnet. If A is the face or pole area of the magentised iron bar, the induction flux density in the rod is
B_i = m/A Wb/m²

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Hence, total flux density in the iron rod consists of two parts [Figure given below].
(i) B₀ –flux density in air even when rod is not present
(ii) B_i –induction flux density in the rod
B = B₀ + B_i = μ₀H + m/A
Eq. (i) above may be written as B = μ_r . μ₀ H = μ_r B₀