P-State Lightwave: Angular Frequency & Amplitude

[cuti_pie75]

Here's the question that I've tried working it out...but sort of blocked at some places:

Write an expression for a P-state lightwave of angular frequency w and amplitude Eo propagating along a line in the xy-plane at 45° to the x-axis and having its plane of vibration corresponding to the xy-plane. At t=0, y=0, and x=0 the field is zero.

And this is what I've done so far...so if anyone can help me out here or tell me if I'm going to the right direction that'll be great.

i got: Eoy = Eo cos45°; Eox=Eo sin45° (in here, I'm not sure if i put the right axis or it's supposed to be Eoy and Eoz)
E(x,t) = Eo cos(kx-wt+1/4π) (once again, i don't know if it's E(x,t) and i assumed that there's no component for the j and k vector)?

kinda lost

 

[SpeedBird]

i think the wave should be propagating in the z direction if it's propagating at 45 degrees to the x-axis, it's also at 45 degrees to the y-axis.

So, i think you're looking for something more like

E(z,t)=Eo Cos(kz-wt) or something..

i've got an exam in the subject in a weeks time and I'm a little lost too :-)

 

[Tide]

The wavenumber is a vector related to the wavelength and corresponds to the direction of propagation so in your case

$$\vec k = \frac {2\pi}{\lambda} \frac {\hat i + \hat j}{\sqrt 2} = \frac {\omega}{c} \frac {\hat i + \hat j}{\sqrt 2}$$

where the latter expression holds only in vacuum so your wave will have components containing sines and cosines of the phase $\vec k \cdot \vec x - \omega t$.

 

[llauren84]

How do you get the sqrt(2)? (nvmd its probably from the new unit vector)

 

[asteriatic]

I would approach this problem by breaking it down into smaller components and using the principles and equations of electromagnetic waves.

First, let's define the P-state lightwave. P-state lightwaves are polarized lightwaves that have their electric field oscillating in a specific plane. In this case, the plane of vibration is the xy-plane.

Next, let's define the given parameters. The lightwave has an angular frequency of w and an amplitude of Eo. It is propagating along a line in the xy-plane at 45° to the x-axis. This means that the wave is traveling in a direction that is 45° from the x-axis, and its electric field is oscillating in the xy-plane.

To express this mathematically, we can use the equation for a plane wave in the xy-plane:

E(x,t) = Eo cos(kx-wt+ϕ)

Where E(x,t) is the electric field at position x and time t, Eo is the amplitude, k is the wave number, w is the angular frequency, and ϕ is the phase angle.

Next, we need to determine the values for k and ϕ. Since the wave is traveling at 45° to the x-axis, we can use trigonometry to determine the values of kx and ϕ.

kx = k cos(45°) = k/sqrt(2)
ϕ = 1/4π

Now, we can rewrite the equation as:

E(x,t) = Eo cos(kx-wt+1/4π)

Finally, we need to determine the value of k. The wave number is related to the angular frequency as k = w/c, where c is the speed of light. Therefore, we can rewrite the equation as:

E(x,t) = Eo cos((w/c)x-wt+1/4π)

This is the expression for a P-state lightwave of angular frequency w and amplitude Eo propagating along a line in the xy-plane at 45° to the x-axis and having its plane of vibration corresponding to the xy-plane. At t=0, y=0, and x=0, the field is zero.

I hope this helps! Let me know if you have any further questions.