If j is normal to a cross-sectional area
A and is constant over the area, the magnitude of the current I through
the area is nevd A 8 Using E = V/l, I = nevd A, and Ohm’s law, one obtains
2
d
eE
ne v
m
ρm
=
The proportionality between the force eE on the electrons in a metal
due to the external field E and the drift velocity vd (not acceleration)
can be understood, if we assume that the electrons suffer collisions
with ions in the metal, which deflect them randomly If such collisions
occur on an average at a time interval t,
vd = at = eEt/m
where a is the acceleration of the electron