This is an exercise of the 2016 admission test of a school of excellence in Pisa (Italy).
None of the students was able to solve it and during the oral session they had the impression that the examiner suggested using the Hall effect.
I read the text in Italian again and it seems to me that...
Homework Statement
In a cylindrical container of radius ## R ## and height ## h \ll R ##, with long axis ## \hat{z} ##, in the presence of gravity acceleration ## \vec{g} = - g \vec{z} ## is contained a neutral ionized gas, whose ions can be described as material points with electric charge ##...