If I place a flat sheet of aluminum foil between a near-field probe and a noisy wire, the sheet completely blocks the noise. However, if that sheet is then wrapped around the wire, it seems to have no effect on the noise. Why?
It's about shield capacitance to earth versus shield capacitance to the noise source aka electric field interference. But....
... If the near field probe were a magnetic loop, things would be different; it wouldn't make much difference where the aluminium sheet was placed because the mag field would get thru the same but, attenuated because of eddy current losses in the aluminium sheet.
So, back to electric fields AND importantly for this question, the aluminium sheet appears to be unearthed. When I say unearthed I mean galvanically unearthed. However, the aluminium sheet will still have capacitance to ground and that capacitance to ground will tend to make it act like a faraday shield. In other words it will block electric fileds and reduce noise pick-up to the near field probe.
If the aluminium sheet were close to the near field probe, then the electric field impinging on it is a bit weaker than if it were close to the noise radiating wire. This is primarily due to distance. This is important to remember.
This means you can regard it as having more capacitance to ground than capacitance to the noise source. Try this for an equivalent circuit: -
In this scenario the noisy electric field trying to hit the probe is dramatically attenuated due to capacitance to earth dominating the capacitance between the noise source and shield. It's a potential divider made from capacitors.
Now, consider the scenario when the shield is really up close to the radiating noise wire. In effect, the shield becomes massively capacitively coupled to the noise source. It "effectively" becomes part of the noise source because the capacitance between it and the noise source is far greater than the capacitance to earth. There is some slight attenuation because there is still some capacitance to ground but basically the aluminium shield re-radiates the noise minus a dB or two.
Without being grounded it does what all shielding would do - it reradiates. When its not wrapped around the wire, the noise is likely being distributed widely enough to reduce the power available to the probe, and hence the reading. Also, as the sheet becomes better coupled to the wire, the more effectively it behaves as an antenna.
If you wrap the sheet around the wire (not grounded), the electric field will almost keep the same shape, but an advantage in this case is that the wire is kept away from the noise outside.
If you wrap the sheet around the wire (grounded), the noise generated by the wire will only be inside of the sheet. So the outside probe will not affected by the noise from the wire.