I haven't gone through this in detail yet, but one misconception is glaring:

Yuri Blanarovich wrote:
. . .
I used 1/2" copper water tubing (non ferrous material passing the magnetic
field) for circular loop about 4 foot diameter. . .

If you believe that, it's no surprise that you're having difficulty
understanding how a shielded loop works.

It's not hard to demonstrate that the (time-varying) magnetic field
doesn't penetrate a non-ferrous shield, if you believe (correctly) that
a time-varying magnetic field will produce a current on a nearby
conductor. Simply put an oscillator or signal source into a copper box
-- you can solder one op out of PC board material. Run some wires all
around the inside which carry the oscillator signal, putting them as
close to the shield wall as you like. Put a battery inside the box to
power the oscillator and seal the box up. Then sniff around the outside
of the box with any kind of magnetic field detector you can devise. If
you have a little potted oscillator of some kind, you should be able to
do this in a couple of hours at most.

Or, just connect your rig to a good dummy load with some double shielded
coax and sniff around the outside of the copper coax shield. If you put
the detector just outside the shield, the current on the inside of the
shield will be much closer to the detector than the current on the
center conductor. So if the shield is transparent to a magnetic field,
your detector should go wild. (Make sure the rig is very well shielded,
though, so no common mode currents make their way from the rig to the
outside of the shield.)

Alternatively, if you'll spend some time with a good electromagnetics
text learning about eddy currents and the like, you'll understand why
you'd be wasting your time with those experiments.

Once you're convinced that the shield blocks the magnetic as well as
electric field, you'll have to revise your theory on how a shielded loop
works. And you'll find that Tom's explanation is correct.

Roy Lewallen, W7EL