# Use of phasor representation in physics

Abel I Daniel
Why do we use phasor representation in physics..For example,why we need maxwells equation in phasor form as well??

## Answers and Replies

Gold Member
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.

Abel I Daniel
ok ,thank you for the reply...what made me ask this question is-i saw maxwells eqautions(electromagnetic) written in phasor form from dpoint form by just substituting d/dt with jw..So what my questin is ,what is the implication of removing that time factor from that equation??

Gold Member
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

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

jason