Refering to:

For me Gibbs is right.

One can't simply consider the two diametrically opposed points of connection as being the terminals of a battery, presenting a potential difference. There is no objective potential difference, not even a potential difference. The voltage is observer dependent.

Induced Emf must be evaluated only along a closed path because it is defined only along a closed path. There is no particular voltage between the two diametrically opposed points until we define the path for the measurement. The fact that the wires connecting the voltmeter are along the B field don't disqualify the rule that want that the emf is defined only along a closed circuit.

If we had a resistance in series with the circular loop and want to know the voltage at the resistance terminals, i.e. the voltage felt by the resistance, we would have to put the voltmeter in parallel with the resistance with no flux crossing in between, in order the resistance and the voltmeter have the same viewpoint, being the same and alone "observer" viewing the same closed path which is both the resistance circuit and the measurement circuit.

The voltmeter being the "observer", it can see only the emf along the closed path of its own measurement circuit. The fact that there is no flux crossing the vertical part of the circuit and the vertical wires are along the B field is an irrelevant data because the emf is given only by dφ/dt, φ being the crossing flux through the surface of the whole circuit.

Here we have 2 loops.

1) We see obviously that some flux crosses the surface of the measurement circuit, as represented by the arrows (presuming the voltmeter is connected to the top).

2) We see that for symmetry reasons, the same flux crosses in equal quantity left and right, so from the voltmeter viewpoint, the resultant flux cancels because each half flux crosses each identical half circuit but in reverse directions. The measure will be zero (1/2*dφ/dt-1/2*dφ/dt).

If one connected a voltmeter directly through the diameter, it will also show zero, for the same reason, and in despite its wires would be othogonal to the B field .

The important point is that an induced emf is defined only on a closed path and that we must never consider that the path could be broken down into independent sections, each one being as a partial source of emf, all being in series. Nature doesn't work this way.

A simple experiment can prove what I say: an single electron near a conductor loop carrying a varying current, doesn't feel any force. It don't move. But if you place billions of electrons around the first loop while imposing them a closed path, they will move. Principle of a transformer. I'm the first surprised.