It is known as the ratio of intensity of magnetization J to the magnetizing force or intensity of the magnetic field (H). It is represented by K.

Mathematically    K = J henry/metre/
                                H

Relation between relative permeability (μ_r) and susceptibility (K)

Total number of lines of induction passing through the material of the magnetic bar = lines due to magnetizing force + lines due to induced magnetism.

  θ = μ_oH X a + m

where a is the pole area of the bar magnet, m is the pole strength of the bar magnet and H is the magnetizing force.

Dividing both sides by a we get

           θ = μ_oH + m
           a              a

or       B = μ_oH + m                      (since θ = B )
                          a                               a

or       μ_oμ_rH = μ_oH + J                 ( since B = μ_oμ_r H and m = J )
                                                                                    a
Dividing both sides by μ_o H we get
            
          μ_r = 1 +   J
                      μ_oH

or        μ_r = 1 + 1   J
                      μ_o  H

or        μ = 1 + K                                  ( Since J  = K )
                     μ_o                                             H


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