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 `v_(d)` is given by Eq. (3.18) `v_(d) = ("I/neA")` 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 metre (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)xx9.0 xx 10^(8)`
`=8.5 xx 10^(28) m^(-3)`
`v_(d)=(1.5)/(8.5xx10^(28)xx1.6xx10^(-19)xx1.0xx10^(-7))`
`=1.1xx10^(-3)ms^(-1)=1.1"mm s"^(-1)`
(b) (i) At a temperature T, the thermal speed* of a copper atom of
mass M is obtained from `[lt (1//2) Mv^(2) gt = (3//2) k_(B)BT]` and is thus typically of the order of `sqrt(k_(B)T//M)` , where `k_(B)` is the Boltzmann constant. For copper at 300 K, this is about `2 xx 10^(2) m//s`. This figure indicates the random vibrational speeds of copper atoms in a conductor. Note that the drift speed of electrons is much smaller, about `10^(-5)` times the typical thermal speed at ordinary temperatures. (ii) An electric field travelling along the conductor has a speed of an electromagnetic wave, namely equal to `3.0 × 10^(8) m s^(-1)` (You will learn about this in Chapter 8). The drift speed is, in comparison, extremely small, smaller by a factor of `10^(-11)`.
