The electron beam in a certain cathode ray tube possesses cylindrical symmetry, and the charge density is represented by v = 0.1/( 2 +

The electron beam in a certain cathode ray tube possesses cylindrical symmetry, and the charge density is represented by ρ_v = −0.1/(ρ² + 10⁻⁸) pC/m³ for 0 < ρ < 3 × 10⁻⁴ m, and ρ_v = 0 for ρ > 3 × 10⁻⁴ m.

(a) Find the total charge per meter along the length of the beam;

(b) If the electron velocity is 5 × 107 m/s, and with one ampere defined as 1C/s, find the beam current.