Joel Kolstad wrote:
"Hence the overall difference between the shielded and unshielded loop
is still a single phase reversal."

Let`s reason together, as Lyndon Johnson used to say. An unshielded wire
loop and/or a same size shield-pipe loop`s outer surface when placed in
the same RF field and having the same attitudes in that field will have
currents which attempt to flow in the same direction. Be it clockwise or
counter-clockwise, it will be the same direction on the outside of both
loops, shielded or unshielded.

As Joel noted, current flowing inside of the shielded loop has its
direction (sense) reversed by the configuration of the shield pipe. As
current flows from outside to inside the loop around the butt ends of
the pipe at the shield gap, there is a phase reversal.

Current flowing on the outside of the shield toward the gap is flowing
away from the gap once it has entered the shield. Also current flowing
on the outside of the shield away from the gap, while it is on the
inside of the shield it is flowing toward the gap. This is a 180-degree
phase reversal between current on the outside of the loop as compared
with that on the inside of the loop, This results just from current
flowing around the butt ends of the shield pipe.

The current inside the loop on the surface of its shield is the primary
current in a two-winding transformer.Current induced into the wire loop
contained by the shield is secondary current in this transformer.

Transformer secondary current is in the same phase as self-induced
current, that is it is 180-degrees out of phase with the primary
current. Two phase reversals in the shielded loop place its output in
the same phase as the unshielded loop.

Best regards, Richard Harrison, KB5WZI