Help Needed: Solve Electromagnetic Problem with Gauss's Law

[chantinh10111]

I need your help, urgent!

Dear all,

Now I got a problem in Electromagnetic class but unfortunately, I have had no solutions for this. I would like to have your help!
Many thanks in advanced.

A uniform plane wave in free space is incident at angle θ on a flat dielectric ε, where ε >ε_o. The planar boundary of the dielectric lies at z=0 and z is normal to the surface, pointing into space. The electric field vector of the incident wave may be expressed as
E_i = E₀(xcosθ + y+ zsinθ)e^{-jkxx + jkzz}
Where E₀ is a real constant.
(a) Show that this incident electric field satisfies Gauss’s Law.
(b) Decompose the incident electric field into its TE and TM components.
(c) What is the polarization of the incident wave?
(d) Determine the expression for the reflected electric field in term of R^TE and R^TM.
(e) For incident angles less than the critical angle θ_c, what are the polarizations of the reflected and transmitted waves?
(f) If ε = 6ε₀, for what angle θ is the reflected wave circularly polarized?

 

[betel]

Hi chantinh, welcome to the forum.
As we will only give you help on your work you will have to tell us what you did so far, or where you exactly have problems.

 

[chantinh10111]

Thanks a lot for your reply.
The problem mentioned above is among my final exam for electromagnetic course. Actually, I did not understand clearly what the teacher talked about the topic in his lecture. So I have no idea for this problem. Thanks a lot if any members can help me with the solution.

 

[betel]

Well, this problem is about the reflection of an electromagnetic wave at a dielectric. Using the Maxwell equations you can derive certain relations between the angles and magnitudes of the vectors.

 

[chantinh10111]

And how can we demonstrate that this incident satisfies Gauss's Law? (#a)

 

[betel]

Could you state the form of Gauss's Law you use?

 

[chantinh10111]

The Gauss's Law is as in the attached file.View attachment Gauss's Law.doc

 

[betel]

So where is your problem applying it to first question.
Do you know what the symbols in your gaus's law mean?
Do you understand what Gauss's law states in words, not just the formula?
I also think the incident field you gave is missing some parts.

 

[chantinh10111]

That is all information my teacher gave to his students to solve this problem. It makes me crazy!

 

[betel]

I don't mean missing as in the teacher didnt give it to you, but you missed something when you typed it here. The field should be a vector, yet you did not give all components.