Page 1 : 170, LEGENDS (MGDN) STUDY MATERIAL I PUC PHYSICS (NCERT)-Electromagnetic Induction, Therefore, mutual inductance of pair of coils is given by,, H.N,N3A,, From (3) and (4), we have, M12 M21, for air core solenoids., %3D, If the solenoids has a core of relative permeability ur, HolM,N,N2 A,, Mention an expression for mutual inductance of two long coaxial solenoids and, explain the symbols, Holl,N;N2 A1, %3D, M is the mutual inductance, µo is the permeability of free space,, Hi is the relative permeability of core of solenoids,, Ni is the number turns of inner solenoid,, N2 is the number turns of outer solenoid,, A1 is the area of cross-section of inner solenoid,, I is the length of each solenoid., where, ADDITIONAL INFORMATION (For CET and understanding the subject), Factors on which mutual inductance depend, Figure-1, Figure-2, Figure-3, The value of mutual inductance depends upon the number of turns of the coils, the, distance between the coils, the geometrical shapes and size of the coils, and also on the, angular orientations between the coils., * If the two coils are wound one over the other as shown in the figure-1, then the, mutual inductance is maximum., * If the coils are perpendicular to other coil as shown in the figure-2, then the mutual, inductance is minimum., * If the coils are arranged as shown in the figure-3, then the mutual inductance lies in, between minimum and maximum value., Coefficient coupling, It is the measure of the coupling between the two coils. It is given by the form, k =M, where Li and L2 are coefficients of self induction of the two coils., M is the coefficient of mutual induction of the two coils., In figure-1, k is maximum. In figure-2, k is minimum., in figure-3, k is intermediate. The value of k lies in between 1 and zero., vhen k, 1, the coupling is perfect and the mutual inductance betw the coiln, %|, naximum., hen k = 0, there is no coupling