# Summary

• Faradayâ€™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.

• Different forms of Faradayâ€™s law

Differential Form:

Integral Form:
• Induced emf for different cases are as follows:

Stationary Loop in Time-Varying Magnetic Field (Transformer emf)

Moving Loop in Static Magnetic Field (Motional emf)

Moving Loop in Time-Varying Magnetic Field (General Induction)

• The displacement current density is given as

• The modified Ampereâ€™s law for time-varying fields is given by considering displacement current density as,

• Maxwellâ€™s equations for time-varying fields are given as follows:
 Differential Form Integral Form
• 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 , and its phasor form  is given as,

• Maxwellâ€™s equations for time harmonic fields are given as follows.
 Differential Form Integral Form
• Time-varying electric scalar potential  and magnetic vector potential  satisfy the inhomogeneous wave equations  and  provided Lorentz gauge condition  is assumed.