A long electron beam has a volume charge density of rhoᵥ(rho) = rhoᵥ₀e⁻ᵖ for rhozu = 0.2cc = 3 x 10⁸ m/s Jᵥ(rho)rhozrho, where rho is the cylindrical radial coordinate. The charge density (i.e., the electrons) is traveling in the z direction with a velocity u = 0.2c, where c = 3 x 10⁸ m/s is the speed of light.
a) Find the current density Jᵥ(rho) at any distance rho from the axis