Magnetic Force on a Wire Carrying a Current

Sections 10.2 through 10.4 dealt with the magnetic force on a SINGLE moving charge. But an electric current in a wire is, physically, an enormous number of individual charge carriers (conduction electrons, in an ordinary metal wire) all moving together with some common drift velocity -- so a current-carrying wire sitting in a magnetic field should, in principle, experience a force that is simply the SUM of the tiny Lorentz forces on every one of its countless individual moving electrons. Deriving this force explicitly, in a usable macroscopic form (in terms of the current $I$ rather than having to track every individual electron), is the task of this section: first for the simplest case of a straight wire segmen …