Problem 3.393

A system consists of a long cylindrical anode of radius \(a\) and a coaxial cylindrical cathode of radius \(b(b< a)\). A filament located along the axis of the system carries a heating current \(I\) producing a magnetic field in the surrounding space. Find the least potential difference between the cathode and anode at which the thermal electrons leaving the cathode without initial velocity start reaching the anode.