Electric field due to a current carrying wire

[AgerPl]

Homework Statement

Circular loop of diameter d located in the vertical plane (x-y) at a distance h from the perfectly conducting half-space. The current source creates a time-harmonic current i(t)=Acos (ωt).

• Find the radiated electric field vector in the plane (x-y) in the far zone of the loop. Assuming that R>>λ
• Find E at the axis z, for any value of this coordinate -∞<z<+∞

Arguments of E are radius vector r and time t.
d<<λ and h<<λ

Homework Equations

The Attempt at a Solution

Should I find the vector magnetic potential and then the magnetic flux density? Like a magnetic dipole and then try to find the electric field?

I know that nabla X B due to a loop far away is = 0.

And regarding the z how I know to where is the axis if he isn't point out in the problem.AgerPl

 

[Simon Bridge]

You find the dircetion of the z axis using your understanding of the cartesian coordinate system and the fact that x and y axes are shown.
If you are unsure how to proceded with the problem - pick a method and give it a try: the point of these problems is that you learn from trying things out. The most important thing to learn is to try things out instead of relying on someone to tell you the best approach.

 

[AgerPl]

Simon, first of all thank you for your answer.

I researched an read some literature and I think I found some nice insights to resolve the problem.
I have to calculate the vector magnetic potential, using that I can infere the magnetic flux density and after I will be capable of getting the electric field intensity. The thing is the fact that I will have to use cartesian or cylindrical coordinates instead of polar ones are really messing with my mind.

I don't know where I will locate the z-axis. Because the professor says that we have an x-y plane and then he asks for the z axis, really ninja stuff that I don't have no insights how to solve.

Can you help me with at least the coordinate system approach?Ager

 

[AgerPl]

After some research and thought I have some conclusions:

• This is a small loop vertical antenna above the surface of the Earth (i.e.)
• The plane x-z is parallel to the surface of the Earth.

Still didn't managed to get more things done. Some help over here?

BR

 

[Simon Bridge]

If you don't know how to find the z axis given the x and y axes you have a serious problem.
Go online and look up "cartesian axes" and look at some pictures.

 

[AgerPl]

I already wrote that I found that x-z axis is parallel to the surface of the PEC conductor.

Still trying to find the influence of the PEC in the small antenna.Regards

 

[Simon Bridge]

Our posts crossed.

 

[Simon Bridge]

So what does the magnetic field do to the loop?
(Is this a section of your course about antennas or just about magnetic fields?)

 

[AgerPl]

Antennas.
More research give me more insights but still can't do the exercise. Really need some help here.

• A small current loop in the far field has the same behavior (in electric field terms) of one small dipole.
• The dipole is horizontally polarized and is from me to the screen. And in his image below the conductor has his polarity reversed, since the tangential component of electric field has to vanish on the conducting plane. The fields are zero in the ground plane.
• I₀=Acos(ωt)=e^-jωt

Thanks for your time.

 

[AgerPl]

Still in need for help