physicscatalyst.com logo




Self Inductance




Self Inductance

  • Consider the figure given below


    Self Inductance

  • When we establish a current through an inductor or coil, it generates a magnetic field and this result in a magnetic flux passing through the coil as shown in figure 1(a).
  • If we vary the amount of current flowing in the coil with time, the magnetic flux associated with the coil also changes and an emf ξ is induced in the coil.
  • According to the Lenz's law, the direction of induced emf is such that it opposes its cause i.e. it opposes the change in current or magnetic flux.
  • This phenomenon of production of opposing induced emf in inductor or coil itself due to time varying current in the coil is known as self induction.
  • If I is the amount of current flowing in the coil at any instant then emf induced in the coil is directly proportional to the change in current i.e.


    where L is a constant known as coefficient of self induction.
  • If (-dI/dt)=1 then ξ=L
    Hence the coefficient of self induction of a inductor or coil is numerically equal to the emf induced in the coil when rate of change of current in the coil is unity.
  • Now from the faraday's and Lenz's laws induced emf is


    comparing equation 1 and 2 we have,

    or Φ=LI
  • Again for I=1, Φ=L
    hence the coefficient of self induction of coil is also numerically equal to the magnetic flux linked with the inductor carrying a current of one ampere
  • If the coil has N number of turns then total flux through the coil is
    Φtot=NΦ
    where Φ is the flux through single turn of the coil .So we have,
    Φtot=LI
    or L=NΦ/I
    for a coil of N turns
  • In the figure given below consider the inductor to be the part of a circuit and current flowing in the inductor from left to right


    Inductor as a part of circuit

  • Now when a inductor is used in a circuit, we can use Kirchhoff’s loop rule and this emf(Self induced emf) can be treated as if it is a potential drop with point A at higher potential and B at lower potential when current flows from a to b as shown in the figure
  • We thus have
    Vab=LdI/dt


Self induction of a long solenoid

  • Consider a long solenoid of length l, area of cross-section A and having N closely wound turns.
  • If I is the amount of current flowing through the solenoid them magnetic field B inside the solenoid is given by,


  • Magnetic flux through each turn of the solenoid is,











Go back to Class 12 Main Page using below links
Class 12 Maths Class 12 Physics Class 12 Chemistry Class 12 Biology





Note to our visitors :-

Thanks for visiting our website.
DISCLOSURE: THIS PAGE MAY CONTAIN AFFILIATE LINKS, MEANING I GET A COMMISSION IF YOU DECIDE TO MAKE A PURCHASE THROUGH MY LINKS, AT NO COST TO YOU. PLEASE READ MY DISCLOSURE FOR MORE INFO.