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Inductance





(9) Mutual Inductance of two co-axial solenoids

  • Consider a long solenoid of length l and area of crossection A containing Np turns in its primary coil
  • Let a shorter secondary coil having N2 number of turns be wounded closely over the central portion of primary coil as shown below in the figure.

     Mutual Inductance of two co-axial solenoids

  • If Ip is the current in the primary coil then magnetic field due to primary coil would be


  • So flux through each turn of secondary coil would be


    where A is the area of crossection of primary coil
  • Total magnetic flux through secondary coil is


  • Emf induced in secondary coil is


    Thus from equation 24

    So




(10) Relation between Mutual inductance and self inductance

  • Consider two coils of same length l and same area of cross-section placed near each other as shown below in the figure

    two coils of same length l and same area of cross-section placed near each other

  • Let there are N1 number of turns in primary coil and N2 number of turns in secondary coil
  • A current I1 in the primary coil produces a magnetic field


    which in turns gives rise to flux?


    in primary coil and


    in the secondary coil due to current in primary coil.
  • By the definition of self induction


    and by definition of mutual induction


  • Reversing the procedure if we first introduce the current I2 in secondary coil then we get


  • So L1 is the self inductance of primary coil,L2 is the self induction of secondary coil and M21=M12=M is the mutual inductance between two coils

  • Product of L1 and L2 is

  • In practice M is always less than eq due to leakage which gives

    Where K is called coefficient of coupling and K is always less then 1.








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