To find the magnitude of the current density, J, when n electrons per
unit volume all move with speed vd, we note that in a time dt the electrons
move a distance vddt, so that nAvddt electrons cross an area A perpendicular
to the direction of electron flow (Fig. 12.12). Since each electron has a
charge e, the charge crossing the area A in the time dt is neAvddt, and the
current density is