Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area `1.0 xx 10^(-7) m^(2)` carrying a current of 1.5 A. Assume that each copper atom contributes roughly one conduction electron. The density of copper is `9.0 xx 10^(3) kg//m^(3)` and its atomic mass is 63.5 u.

Explanation

The direction of drift velocity of conduction electrons is opposite to the electric field direction, i.e., electrons drift in the direction of increasing potential. The drift speed `upsilon_(d)` is given by Eq.
`I Delta t = n eA//V_(d)//Delta t`
`V_(d) = (I//n eA)`
Now, `e = 1.6 xx 10^(-19) C,A = 1.0 xx 10^(-7) m^(2), I = 1.5 A`. The density of conduction electrons n is equal to the number of atoms per cubic meter (assuming one conduction electron per Cu atom as is reasonable from its valence electron count of one). A cubic metre of copper has a mass of `9.0 xx 10^(3)` kg. Since `6.0 xx 10^(23)` copper atoms have a mass of 63.5 g
`n = (6.0 xx 10^(23))/(63.5) xx 9.0 xx 10^(6)`
`= 8.5 xx 10^(28) m^(-3)`
Which gives,
`upsilon_(d) = (1.5)/(8.5 xx 10^(28) xx 1.6 xx 10^(-19) xx 10 xx 10^(-7))`
`= 1.1 xx 10^(-3) ms^(-1) = 1.1 m m s^(-1)`