Problem: Find the drift velocity of the electrons in an aluminum wire of diameter 0.800 mm at 45^oC if the current is 5 amperes. What field (over a 3 m length of the wire) is required to cause this current?

First, several items have to be assembled from tables...

mass density of aluminum = 2.7 g/cm³

molecular weight = 26.98 g/gmole

Avogadro's number = 6.022 x 10²³ "things"/gmole

("things" can be atoms, molecules, particles, electrons, whatever)

Aluminum contributes one electron per atom to conduction

resistivity at 20 ^oC is 2.82 x 10^-8 ohm m

temperature coefficient of resistivity is 3.90 x 10^{-3 o}C^-1

a) In the work that follows, dimensional analysis (rather than substitution into formulas) is being used:

n = electrons per unit volume:

The current has to come out in amperes. Starting with n, the electrons per unit volume, we would need the charge on each electron to get coulombs. Since amperes = C/s, multiplying by the drift velocity of the electrons (m/s) and the cross-sectional area (m²), takes care of the units, resulting in C/s:

b) For the field, we use the approximation that the field is uniform (the cross-sectional areas, to the electrons, appear to be infinite plates). We also need a few other formulas:

First, I find the resistivity at 45^oC, plug it into the last equation to get the resistance. Then I use the second formula (Ohm's Law) to find the voltage difference between the two ends of the wire. Finally, the first formula provides the field E.