Cylindrical containing a neutral ionized gas
In a cylindrical container of radius $\displaystyle R$ and height $\displaystyle h \ll R$, with long axis $\displaystyle \hat{z}$ , in the presence of gravity acceleration $\displaystyle \vec{g}=−g \vec{z}$ is contained a neutral ionized gas, whose ions can be described as material points with electric charge $\displaystyle q>0$ and mass $\displaystyle M$ (heavy positive ions) and material points with electric charge $\displaystyle −q$and mass $\displaystyle m<M$ (light negative ions). The system is maintained at a constant and uniform temperature, and it is assumed for the sake of simplicity that the ions can not bind to each other by neutralizing themselves. Discuss qualitatively the distribution of ions in equilibrium conditions and calculate, in particular, the value of the electric field inside the cylinder.
