Dear Andy, Jim, LF Group,

1. My strong support for what Jim has said.  The immediate environment always affects all field measurements, not just magnetic field measurements.
2. Marcus’s formula is correct for free-space and it is in all the books. Wire loss is not an issue for a typical open-circuit loop.
3. In an ‘environment’ near real ground, buildings etc., the ‘physics’ insists that such a loop gives an open circuit voltage proportional to B = mu * H.  The presence of the environment means that mu is not equal to the free-space value of mu(0). 
4. The current in a short-circuit lossless loop is directly proportional to the H field and it does not depend on the area.  This is not in ‘the antenna books’, but it is in some physics books dealing with super-conductivity. 
5. There is a third case and this is when the loop is resonant.  If the loop is loss-less and therefore 100% efficient and power matched to the load of the measuring detector.  The ‘physics’ demands that the antenna ‘capture cross-section’ should be the same as the capture cross-section of any short dipole.  In free-space this is 1.5 / 4pi square wavelengths. The received power is the (average) power density times this (small dipole) cross-section area. The free-space equivalent E and H fields can be found directly from this.  This measurement is irrespective and independent of (loss-less) loop size.  The ‘proof’ of this is in the better antenna books, such as Kraus and Balanis. 
   What the system Q ends up being does not matter for this proof.  Some may have noticed however that it is a matter of considerable (unnecessary) dispute, as reported in the pages of RadCom. However loop (or any antenna) losses do matter, because the cross-section area of an antenna is reduced in proportion to its (in)efficiency.  This point is in most of the antenna books.   After real conductor losses have been minimised and factored out we find practical outdoor Qs of 100 to 350.  In a screened room the loop Q can exceed 600. 
6. There are similar arguments for short-circuit, open-circuit and resonant electric field measuring ‘whip’ antennas. 
7. Thus you have six choices for measuring the fields of an antenna in a real environment.  Only in free space do all six methods give the same answer.

I hope that this is useful and of interest.  It just goes to show that real life can be hard and difficult, but more fun than just theory on its own.  Also it has not “all been done before!”

Mike -  G3LHZ