Question regarding Hall sensor/effect wrt q(VxB)

Lighthouse

If a make some basic assumptions about a standard hall probe I find, quite expectedly that the velocity of the charge carriers is of the order 10-5 m/s. In a hall probe measuring the earths magnetic field like the one in my phone this should be the velocity of the charge carriers with respect to the earths field (using q(VxB)). But it isn't not if Im walking around. If I include the velocity I'm giving the charge carriers then the sensor shouldn't work, but it does. Why is that?


I think its because the hall effect creates a compensating voltage across the voltage sensor as well as the hall sensor since both are moving in the same way but I'm not sure if that's easy to do. Ie is the hall voltage material dependent?