Switching the position of voltage probes changes the sign of the measured voltage. How can you determine the charge sign in a Hall effect then? When you measure the voltage in a battery, for example, you place the voltage probes at the battery ends and get, let's say, a reading of 1.5V. If you change the position of the probes in regards to the battery ends, you will then measure -1.5V.
Now, in a Hall measurement, you have control of electric current and the magnetic field, and you use the sign of the measured Hall voltage to determine the sign of the charge carriers, right? If, however, you switch the positions of the voltage probes you will change the sign of the measured voltage. How can you tell then if the charge carriers have a positive or a negative sign?
Thank you very much.
 A: Yes the sign changes, but based on your voltmeter you will still be able to tell which point is at a higher potential and which is at a lower potential. This doesn't depend on where your electrodes are at. In other words, it doesn't matter if you have found that
$$\Delta V=V_b-V_a>0$$
or
$$-\Delta V=V_a-V_b<0$$
Either way you still know that $V_b>V_a$. Switching your probes doesn't alter the system. It would be like me asking how do we know which direction gravity points if when I stand on my head the force changes direction. If I'm on my feet or on my head I still know that the force pulls me towards the center of the Earth, so the above objection isn't valid here.
Therefore, there is no issue with determining the charge carrier sign with the.Hall effect. As long as you know what a positive or negative reading means for your probe positions then you can easily determine which probe is at a higher potential and thus the sign of the charge carrier based on how you set up the rest of the system.
