An axial electric field E = Eẑ and a radial magnetic field B = Bp̂ coexist in the volume V between two short cylindrical shells concentric with the z-axis. Suppose V is filled with xenon gas and, at a given moment, a discharge ionizes the gas into a plasma composed of n_e electrons per unit volume and n_i = n_e singly charged positive ions per unit volume. This is a model for a propulsion device used on spacecraft.

(a) Show that the electrons drift at constant speed in the axial direction because they acquire a velocityv = (E × B)/B². This defines a Hall current density j_Hall = −en_ev.(b) Argue that the cylindrical shells experience a net thrust (force) T = B × j_Hall because the ions are ejected from V . What about the Lorentz force on the ions?

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