TEM wave radiation from a solenoid with cylindrical symmetry

[yungman]

I am trying to figure out how the TEM wave looks like and how it propagate outward. Attached is a pdf of a drawing with only the solenoid and show the winding that the current is flowing in CCW and a reference. Also I draw a loop with one resistor and show the induced current and the polarity of the resistor for follow up question.

This is my thinking:

The magnetic flux line is shown in blue that loop from the top back to the bottom. I draw just two loops, but it is understand it is all around 360 deg around the z axis(symetric around the z axis or:

$$\hbox { Both }\frac {\partial \vec E}{\partial \phi} \;=\; \frac {\partial \vec B}{\partial \phi} \;=\; 0 \hbox { in cylindrical coordinates. }$$

I think the associate electric field look like the red circle. The circles are parallel with the xy plane. The direction of propagation of each point move as shown in direction of the $\hat n$ at every point. The direction of $\hat n$ is:

$$\hat n \;=\; \vec E X \vec B$$

basically, I think the propagation of the TEM is outward in direction of the $\hat n$ at all points. tell me whether I am correct.

Feel free to download the pdf and draw what you think is right and post it back.

Furthermore, I would like to see how the varying magnetic field induce current and voltage into the loop with resistor. I know we have Faraday's Law, I just want to see the machenism.

thanks for the help

Alan

 

[cmos]

You're drawing looks pretty good to me; maybe that's why you have no replies, because there's nothing more to say!

I just want to point out a few things because you didn't explicitly state them; although, I have a feeling that you know you've made certain assumptions.

First of all, you have assumed an AC current. If you were using a DC current, your picture would still be correct minus the fact that you would have no electric field. With an AC current, the common interpretation is that the lines of B will close in on themselves (form closed loops) as polarity changes. This is similar to the case of an oscillating electric dipole and its lines of E.

As for the lines of E in your picture, I like to think of them as lines of latitude on a sphere. Thus at the two poles, you would have lines of zero circumference. Each "change in polarity" can be pictured as the introduction of a new sphere, with lines of latitude (lines of E) pointed in the opposite direction as the preceding sphere. Thus radiation can be pictured by an increase in each sphere's radius. Note that no matter how big the sphere, you will always have loops of zero circumference at the poles, consistent with zero radiation along the z-axis.

Second point, everything you and I have said is strictly applicable only if the solenoid is small, i.e. if the circumference of the solenoid is much less than the wavelength. If this condition does not prevail, then you can have a much different picture arising from phase retardation, i.e. constructive and destructive interference due to fields being spatially separated throughout points on the solenoid. If this point interests you, then I'll refer you to the internet; look up end-fire helical antennas.

 

[yungman]

You're drawing looks pretty good to me; maybe that's why you have no replies, because there's nothing more to say!

I just want to point out a few things because you didn't explicitly state them; although, I have a feeling that you know you've made certain assumptions.

First of all, you have assumed an AC current. If you were using a DC current, your picture would still be correct minus the fact that you would have no electric field. With an AC current, the common interpretation is that the lines of B will close in on themselves (form closed loops) as polarity changes. This is similar to the case of an oscillating electric dipole and its lines of E.

As for the lines of E in your picture, I like to think of them as lines of latitude on a sphere. Thus at the two poles, you would have lines of zero circumference. Each "change in polarity" can be pictured as the introduction of a new sphere, with lines of latitude (lines of E) pointed in the opposite direction as the preceding sphere. Thus radiation can be pictured by an increase in each sphere's radius. Note that no matter how big the sphere, you will always have loops of zero circumference at the poles, consistent with zero radiation along the z-axis.

Second point, everything you and I have said is strictly applicable only if the solenoid is small, i.e. if the circumference of the solenoid is much less than the wavelength. If this condition does not prevail, then you can have a much different picture arising from phase retardation, i.e. constructive and destructive interference due to fields being spatially separated throughout points on the solenoid. If this point interests you, then I'll refer you to the internet; look up end-fire helical antennas.

Thanks for you reply. Yes I am just based on a very simple model. Yes I under that when polarity of E change, it is like the circle is circulating in opposite direction. Thanks for all your help. This is kind of a spin off topic from the big MIT professor thread where we really going at it. Feel free to join in there.