When two coils are placed near each other, all the flux produced by one coil does not link with the other coil, as assumed in Art only certain portion say, K)of flux produced by one coil links with the other coil, K being less than unity, K is called the coefficient of coupling.

Flux created in coil A due to current of i₁ amperes, ∅₁ =  N₁i₁  Wb
                                                                                  l / μ_oμ_ra

Flux linking with coil B, ∅₂ = K∅₁ = KN1i₁  Wb
                                                      l / μ_oμ_ra

Coefficient of mutual induce, M = KN₁N₂
                                               l / μ_oμ_ra
Coefficient of self inductance of coil  A, L₁ = N₁∅₁ =  N₁²
                                                                 i₁       l / μ_oμ_ra 

Coefficient of self inductance of coil B, L2 = N₂∅₂  =   N₂²
                                                                                       i₂          l / μ_oμ_ra 

Multiplying expressions and taking square root we get



Comparing expressions and we get



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