What is the phasor form for an E field with a variable distance and phase shift?

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SUMMARY

The phasor form for the electric field E = uniti Asin[w(t-z/c)+pi/4] is definitively represented as unit i Aexp(j pi/4). In phasor analysis, the time-dependent component exp(jwt) is omitted, focusing instead on the spatial variable z. The transformation from the sine function to cosine is crucial, as it allows for the correct representation of the phasor as A exp(-jkz) for the wave function A cos(wt - kz + ψ).

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cutesteph
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If I am given an E field E = uniti Asin[w(t-z/c)+pi/4].
Is the phasor form = unit i Aexp(j pi/4) or unit i Aexp(-j(wz/c - pi/4) ?
 
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The phasor of a function (wave) containing variables other than time, in this case distance z, is I believe represented by a function including z but not t.

So the phasor of A cos(wt - kz) would be A exp(-jkz) as the time function is Re{A exp j(wt - kz)}. The exp(jwt) is left out of the phasor expression since in any equation using phasors that term cancels out. At least that's been my experience with e-m wave phasors.

So if the time function is A sin(wt - kz + θ), what do you think the phasor is?
Hint: change your time function to read A cos(wt - kz + ψ).
 

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