Use of phasor representation in physics

Phasors are good for waves of constant frequency ... hence electrical engineers use them for AC circuits, and they use them a lot.

So you will probably only use phasors while studying AC circuits; they are useful only for linear systems.

 

They were working in frequency space ... same place you go with the Laplace transform, or its cousin the Fourier transform.

In this case they assumed that the electromagnetic field was a harmonic wave - and plugged this into Maxwell's equations - leaving you with the "Phasor form of Maxwell's equations".

Here is a lecture which includes the derivation: http://ivp.ee.cuhk.edu.hk/~ele3310/data/ELE3310_Tutorial_10.pdf

 

Another reason is that properties of media are "easy". For example, for electric field:
[tex]
\mathbf{D} = \epsilon_0 \mathbf{E} + \mathbf{P}
[/tex]
but it is only for a single frequency that
[tex]
\mathbf{P}(\omega) = \epsilon_0 \chi_e (\omega) \mathbf{E}(\omega).
[/tex]
In the time domain we in general have a convolution,
[tex]
\mathbf{P}(t) = \epsilon_0 \int^t d\tau \, \, \, \chi_e (\tau) \mathbf{E}(t-\tau).
[/tex]

jason

 

You can assume a time dependence of exp(jwt) without losing generality due to the principle of superposition. For incident fields with multiple frequency components, you can solve Maxwell's equations for each frequency component, then sum the solutions at the end as required.

Claude.