Self Inductance

Self Inductance

• Consider the figure given below
  
  
  
  
  
• 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
  Φ_tot=NΦ
  where Φ is the flux through single turn of the coil .So we have,
  Φ_tot=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
  
  
  
  
  
• 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
  V_ab=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,
  
  
  

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• Notes
  • Inductance
  • Self Inductance
  • Energy in an inductor
  • Growth and decay of current in L-R circuit
  • The R-C circuit
  • The L-C circuit
  • Mutual Inductance

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