Maxwell's Equations for TimeVarying Fields
In addition to his contribution of displacement current, Maxwell brought together the four basic laws governing electric and magnetic fields into one set of four equations which, as a set, completely describe the behaviour of any electromagnetic field. All of the vector field, flux, current and charge terms in Maxwellâ€™s equations are, in general, functions of both time and space [e.g., E (x, y, z, t)]. The form of these quantities is referred to as the instantaneous form (we can describe the fields at any point in time and space). The instantaneous form of Maxwellâ€™s equations may be used to analyse electromagnetic fields with any arbitrary time variation.Maxwellâ€™s equations
Sl. No.  Differential Form  Integral Form  Name 
1.  Gaussâ€™ law of electrostatics  
2. 
Gaussâ€™ law of magnetostatics
(nonexistence of magnetic monopole) 

3.  Faradayâ€™s law of electromagnetic induction  
4.  Modified Ampereâ€™s circuital law 
Time Harmonic Fields
Time harmonic fields are those fields that vary sinusoidally with time. They are easily expressed in phasors.Maxwellâ€™s Equations for TimeHarmonic Fields
To transform the instantaneous Maxwellâ€™s equations into timeharmonic forms, we replace all sources and field quantities by their phasor equivalents and replace all time derivatives of quantities with jÏ‰ times the phasor equivalent. Thus, the Maxwellâ€™s equations for time harmonic fields are given in the table.Maxwellâ€™s equations for time harmonic fields
Sl. No.  Differential Form  Integral Form  Name 
1.  Gaussâ€™ law of Electrostatics  
2. 
Gaussâ€™ law of Magnetostatics
(nonexistence of magnetic monopole)


3.  Faradayâ€™s law of electromagnetic induction  
4.  Modified Ampereâ€™s circuital law 