# Electric field due to a current carrying wire

1. Jan 12, 2016

### AgerPl

1. The problem statement, all variables and given/known data

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
2. Relevant equations

3. 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.

Best regards,
AgerPl

2. Jan 14, 2016

### 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.

3. Jan 14, 2016

### AgerPl

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?

Best regards,
Ager

4. Jan 14, 2016

### 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

5. Jan 14, 2016

### 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.

6. Jan 15, 2016

### AgerPl

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

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

Regards

7. Jan 17, 2016

### Simon Bridge

Our posts crossed.

8. Jan 17, 2016

### Simon Bridge

So what does the magnetic field do to the loop?

9. Jan 19, 2016

### 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