Shielding a single AC current carrying wire.

[broli]

I was thinking whether it was possible to shield a portion of a circuit that has only a single conductor without a return path. The frequency is high enough for the Earth's capacitive impedance to be low.
Is my assumption then correct that the induced voltage in the shield will create a displacement current that will be opposite to the alternating current going through the wire, canceling some of the magnetic field of the wire?

 

[mfb]

I don't see why you would expect a significant induced voltage in the shielding wire. And even if you have this, the small capacitance will lead to a small current.

 

[broli]

I would suspect a significant voltage due to inductive coupling. And I know the capacitance is small however if we work with mhz frequencies the impedance of the capacitor should drop significantly too?

 

[sophiecentaur]

Is the picture that you posted a real representation of the situation or is it just a 'schematic'?

No piece of wire acts independently of another conductor or 'Ground'. Your wire will be part of a transmission line, either balanced or unbalanced, carrying power from A to B and it will have a characteristic impedance - as will the transmission line composed of the cylinder and the length of wire inside it. Even a vertical wire antenna is only working because of currents that also flow to Earth.
It is difficult to be sure that any 'equivalent' model one proposes for this sort of system is appropriate and it is easy to miss out the main mechanisms at work. One way of looking at your setup is to regard the sleeve / screen as a parasitic element. This will have currents which flow along the outside as well as the inside of the cylinder. The length of this cylinder (in wavelengths) will greatly affect the value of the currents so it is difficult to predict anything definite unless the setup is better defined.
IMO, except in every circumstance, the actual 'screening' effect of the sleeve would be very small - rather changing any pattern of radiation from the wire (as an antenna) than any other function.

OTOH, a quarter wave long sleeve which is shorted to the wire at the far end can act as a 'choke' and limit the current flowing. This is a method used on some antenna down-leads to limit current flowing down the outer of the coax.

BTW, the 'capacitive coupling' referred to could be equivalent to a 'capacitative potential divider'. The capacity between sleeve and wire could be a lot higher than the capacity to Earth so the sleeve could be very nearly at the same potential as the wire.

 

[broli]

Thank you for the feedback sophiecentaur, yes the picture is close to a real representation however I have to state that the length of the sleeve is a couple orders of magnitude below wavelength. We're talking about lengths of perhaps 20cm for the sleeve at frequencies ranging from 40khz-1Mhz. So if you want to see it as an antenna then it would be a very short one.

 

[sophiecentaur]

OK, in that case, it is going to be capacitatively coupled to the wire by, perhaps 10pF (ballpark figure). But where is the 'other' conductor? There has to be a return path unless you're dealing with radiated power and a standing wave on your wire.
As the sleeve is such a small fraction of a wavelength, that's about the only thing that will happen. The current induced will be vanishingly small because there is no significant phase difference along its length and (as a dipole) it's too short to act as a significant parasitic. If you want to screen, you can Earth the sleeve somewhere and it will bring the E field to zero outside and induce some current in the Earth lead.
A bit of real context could probably help in answering usefully. You presumably have identified a problem of crosstalk or coupling between two circuits? Is there any reason why this single conductor needs to be on its own out in the middle of space and not part of some co-ax or a twisted pair? You have a large current loop, as it is and a bit of conductor near it isn't going to alter the field around it significantly, Imo.

 

[broli]

Well it should mostly be voltage caused by induction however since the shield is not part of a closed loop the current will indeed be minimal. My goal is to try and get the shield/earth current as high as possible without having to resort to a ground loop or using a return path. And it's not part of any practical setup besides a benchtop experiment really.
Would adding more insulated layers to the shield, as into increase the surface area help at all?

 

[sophiecentaur]

As far as I can see, the screen, connected to Earth is going to behave more or less like a simple capacitor (tens of pF) connected to Earth on one side of the generator, which will just unbalance the circuit a small amount. It is hardly likely to affect the magnetic field in the loop and, as the loop is small compared with a wavelength (thus, a very low impedance), the E field will be very low. (The resistance of the loop is small, I assume).

You could, I guess, load the screening tube with a tuned circuit and affect the H field by increasing the parasitic current. That would have the effect of increasing the impedance seen by the generator, I think, which would just reduce the current in the loop. But you could achieve this by reducing the power from the generator.