Phasors

Whenever a problem is time-harmonic the fields can be written in the form

Instead of using a cosine function for the time dependence, it is more convenient to use an exponential function, by writing the field as

is a phasor, which contains amplitude and phase information of the field but is independent of t. One thing that makes the use of phasors suitable is that a time derivative corresponds to a multiplication by jω:

If the fields satisfy a linear time-dependent equation, then the corresponding phasors must satisfy a similar equation in which the time derivatives are replaced by a factor jω. All time-harmonic equations are expressed as equations for the phasors. (The tilde is dropped from the variable denoting the phasor.)

The frequency domain formulation is only applicable for equations linear in the fields. In particular, it cannot be used with materials whose properties depend on the fields themselves (nonlinear materials). See Effective Nonlinear Magnetic Constitutive Relations for a formulation that approximates nonlinear magnetic constitutive relations in time-harmonic problems.


	When analyzing the solution of a time-harmonic equation, it is important to remember that the field that has been calculated is a phasor and not a physical field. For example, all plot functions visualize by default, which is E at time t = 0. To obtain the solution at a given time, specify a phase factor in all results settings and in the corresponding functions.