An election beam shaped like a circular cylinder of radius r0 carries a charge density giv...

An election beam shaped like a circular cylinder of radius r0 carries a charge density given by

where ρ0 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.

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(b) If the electrons are moving in the +z-direction with uniform speed u, determine the magnitude and direction of rhe current crossing the z-plane.