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

In summary, the phasor of a function with variables other than time, such as distance, is represented by a function including those variables. This is why the phasor of E = uniti Asin[w(t-z/c)+pi/4] is either unit i Aexp(j pi/4) or unit i Aexp(-j(wz/c - pi/4) depending on the variables being used. In the case of A sin(wt - kz + θ), the phasor would be A exp(-jkz + jθ) or A exp(-jkz - jψ) when written as A cos(wt - kz + ψ).
  • #1
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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  • #2
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).
 

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

What is the phasor form of an E field?

The phasor form of an E field is a mathematical representation of the electric field that takes into account both the magnitude and phase of the field. It is often used in the study of electromagnetic waves and circuits, allowing for simpler calculations and analysis.

How is the phasor form of an E field different from the standard form?

The standard form of an E field only considers the magnitude of the field, while the phasor form also takes into account the phase. This allows for a more comprehensive representation of the electric field and its behavior over time.

What is the significance of the phase in the phasor form of an E field?

The phase in the phasor form of an E field represents the relative timing of the field compared to a reference signal. This is important in analyzing the behavior of electromagnetic waves and circuits, as the phase can affect the amplitude and frequency of the signal.

How is the phasor form of an E field used in circuit analysis?

The phasor form of an E field is often used in circuit analysis to simplify calculations and better understand the behavior of electric fields in circuits. By converting the time-dependent electric field into a steady-state phasor form, the analysis becomes more intuitive and can provide valuable insights into the circuit's behavior.

Can the phasor form of an E field be used for all types of electric fields?

Yes, the phasor form of an E field can be used for all types of electric fields, including sinusoidal, constant, and time-varying fields. It is a versatile mathematical tool that can aid in the analysis of various electromagnetic phenomena.

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