An electron beam coming from an electron gun consists of electrons that are uniformly distributed within a cylindrical region of space having a radius a = 1 [mm]. The axis of the cylinder is along the z axis, and the electrons are moving with a velocity vector v in the positive z direction. The velocity of the electrons is 0.1c where c is the speed of light (2.99792458 ´ 108 [m/s]). The magnitude of the current in the beam is 1 Amp.
a) Calculate the current density vector
b) Calculate the volume charge density Pv0 inside the electron beam.
c) Calculate the spacing between the electrons, assuming that they are arranged on a rectangular cubical lattice, with spacing between adjacent electrons in the x, y, and z directions.