E from a line of moving charges **
An essentially continuous stream of point charges moves with speed v along the x axis. The stream extends from −∞ to +∞. Let the charge density per unit length be λ, as measured in the lab frame. We know from using a cylindrical Gaussian surface that the electric field a distance r from the x axis is E=λ/2πϵ0r. Derive this result again by using Eq. (5.15) and integrating over all of the moving charges. You will want to use a computer or the integral table in Appendix K.