How to find which polarization ?

[athithi]

how to find which polarization ??

a classical charged particle moving with frequency 'w' in a circular orbit of radius 'a' centerd at the origin in the x-y plane, em radiation. At points (b,0,0) and (0,0,b) where b >> a the em waves are

1. circularly polarised and elliptically polarised respectively
2. circularly polarised and plane polarised respectively
3. plane polarised and circularly polarised respectively
4. plane polarised and elliptically polarised respectively

the answer is given to be "plane polarised and circularly polarised respectively" ...
Can anyone help how to solve this kind of problems?

Thanks in advance !

 

[Meir Achuz]

The polarization (locus of the E vector) will have the same shape as the circular orbit looked at from that direction. In the plane of the orbit, the polarization is linear.
Straight up from the plane of the orbit, the polarization is circular. At angles in between, it is ellliptical, just as the circle looks.

 

[kerimek]

To solve this problem, you can use the equations for circular and elliptical polarization to determine the polarization at the given points. For circular polarization, the electric field vector rotates at a constant rate around the direction of propagation. This can be represented by the equation E = E0cos(wt - kz), where E0 is the amplitude, w is the angular frequency, t is time, and k is the wave vector. For elliptical polarization, the electric field vector rotates at a changing rate, resulting in an elliptical shape. This can be represented by the equation E = E0cos(wt - kz)e^(iδ), where δ is the phase difference between the two components of the electric field.

To find the polarization at the given points, you can calculate the phase difference between the two components of the electric field at each point. At point (b,0,0), the phase difference would be 0, indicating circular polarization. At point (0,0,b), the phase difference would be π/2, indicating elliptical polarization. Therefore, the correct answer is plane polarized and circularly polarized at points (b,0,0) and (0,0,b) respectively.

It is also important to note that at point (b,0,0), the electric field vector would be perpendicular to the plane of the orbit, resulting in plane polarization. At point (0,0,b), the electric field vector would be parallel to the plane of the orbit, resulting in circular polarization. This can also help in determining the correct answer.

In general, to find the polarization of a wave, you can analyze the direction and amplitude of the electric field vector at different points in space. This will help determine if the wave is linearly polarized, circularly polarized, or elliptically polarized.