Plane wave equation of linear polarization

[geft]

Question 1

Basically I have no idea how to calculate the z part of the equation since x and y are assumed to be propagating in the z direction.

 

[rude man]

Question 1

Basically I have no idea how to calculate the z part of the equation since x and y are assumed to be propagating in the z direction.

Why do you assume it propagates in the z direction? It's just a superposition of three E fields. Not going anywhere.

 

[geft]

I may be wrong but according to my textbook E(r,x) is the plane wave where r is the direction of propagation. For E0cos(wt-kz) z seems to be the direction.

 

[rude man]

I may be wrong but according to my textbook E(r,x) is the plane wave where r is the direction of propagation. For E0cos(wt-kz) z seems to be the direction.

Certainly. But your E field is not a plane wave. A plane wave does not have a field component in the direction of propagation.

 

[geft]

Thanks, that z component certainly confused me and now I see why. Does that mean I'm unable to convert it to the (wt-kz) format?

 

[rude man]

Thanks, that z component certainly confused me and now I see why. Does that mean I'm unable to convert it to the (wt-kz) format?

Right.

The expression given you is in what are called 'phasors', at least in ac theory. In any case you are apprently expected to know what the exponentials signify.

The expression given you has as its "measurable" equivalent

E_x sin(wt + phi1) + E_y sin(wt + phi2) + E_z sin(wt + phi3)
where the phi are the phase angles associated with each of the three E field components.

(You could also substitute cos for sin here; that is a matter of what is defined as t = 0 and is not an identifiable part of the given equation. The meaning of the three phase angles is really only how they relate to each other. It should be obvious that when you measure this field there is no such thing as "t = 0".)

So can you identify the E_x etc. coefficients and the respective phase angles from the given phasor expression?

 

[geft]

So basically phi1 = 30, phi2 = -50 and phi3 = 210; the E_x etc. are the respective amplitudes; and the coefficients.. what coefficient? Wouldn't k be removed since the field is not a plane wave and thus the direction component is 0? I'm not sure how to factor in the frequency either since I think t remains as a variable.

 

[rude man]

So basically phi1 = 30, phi2 = -50 and phi3 = 210; the E_x etc. are the respective amplitudes; and the coefficients.. what coefficient? Wouldn't k be removed since the field is not a plane wave and thus the direction component is 0? I'm not sure how to factor in the frequency either since I think t remains as a variable.

I see you're still hung up on k. There is no k.

Look at the end coefficient e^jωt. What does the ω stand for?

 

[geft]

2pi.f? Does that mean I should just substitute 100MHz into f to get the final answer? What of t?

 

[rude man]

2pi.f? Does that mean I should just substitute 100MHz into f to get the final answer? What of t?

You should have been taught the meaning of e^jωt. It represents a sinusoid of radian frequency ω. If you take the real part of it you get cos(ωt) so you have a time-dependent expression in your E field.

Your E field in summary consists of three components, each with its own amplitude and phase angle, and varying with time as cos (ωt).

And yes, f = ω/2π = 100 MHz here.

 

[geft]

Thanks for the help. Yes, I was taught of it but I just wasn't able to make the connection.