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  • Faraday’s law states that the emf induced in a closed circuit is proportional to the rate of change of the magnetic flux linkage and the direction of the current flow in the closed circuit is such that it opposes the change of the flux.
    Description: 17663.png
  • Different forms of Faraday’s law
    Differential Form: Description: 18332.png
    Integral Form: Description: 16745.png
  • Induced emf for different cases are as follows:
    Stationary Loop in Time-Varying Magnetic Field (Transformer emf)
    Description: 18066.png
    Moving Loop in Static Magnetic Field (Motional emf)
    Description: 18174.png
    Moving Loop in Time-Varying Magnetic Field (General Induction)
    Description: 45016.png
  • The displacement current density is given as
    Description: 17419.png
  • The modified Ampere’s law for time-varying fields is given by considering displacement current density as,
    Description: 17101.png
  • Maxwell’s equations for time-varying fields are given as follows:
    Differential Form Integral Form
    Description: 31717.png Description: 31712.png
    Description: 31705.png Description: 31700.png
    Description: 31692.png Description: 31685.png
    Description: 31674.png Description: 31666.png
  • Time harmonic fields are those fields that vary sinusoidally with time. They are easily expessed in phasors. 
  • The relation between a time-harmonic field vector Description: 18482.png, and its phasor form Description: 18565.png is given as,
    Description: 17762.png
  • Maxwell’s equations for time harmonic fields are given as follows.
    Differential Form Integral Form
    Description: 27706.png Description: 27702.png
    Description: 27697.png Description: 27692.png
    Description: 27728.png Description: 27717.png
    Description: 27731.png Description: 27738.png
  • Time-varying electric scalar potential Description: 16969.png and magnetic vector potential Description: 19416.png satisfy the inhomogeneous wave equations Description: 18584.png and Description: 19295.png provided Lorentz gauge condition Description: 17367.png is assumed.

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