An electron beam shaped like a circular cylinder of radius r0 carries a charge density given by rhov = (−rho0/1 + r^2) (C/m^3),
where rho0 is a positive constant and the beam’s axis is coincident with the z axis.
(a) Determine the total charge contained in length L of the beam.
(b) If the electrons are moving in the +z direction with uniform speed u, determine the magnitude and direction of the current crossing the z-plane.