(a) Estimate the average drift speed of conduction electrons in a copper wire of cross sectional area `1.0xx10^(-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 `9.0xx10^3 kgm^(-3)` and its atomic mass is `63.5 u.` (b) Compare the drift speed obtained with the speed of propagation of electric field along the conductor, which causes the drift motion.

Explanation

Here, `A= 1.0 xx 10^(-7) m^(2)` ,
`I = 1.5 A, d=9.0 xx 10^(3)kg//m^(3)`
Atomic mass, `M=63.5 u=63.5 kg`
Avogadro's number, `N=6.0 xx10^(26)` per kg atom Number of atoms per unit vloume in the given copper wire
`=(N)/(M//d) = (Nd)/(M)`
As one atom contributes one conduction electron, therefore, number of conduction electrons per unit volume or number density of conduction electrons in the given copper wire is
`n=N/M d=(6.0 xx 10^(26) xx9.0 xx10^(3))/63.5 = 8.5 xx 10^(28) m^(-3)`
`v_(d) =(I)/("neA")`
`=91.5/((8.5 xx10^(28))xx(1.6xx10^(-19)) xx(1.0 xx10^(-7)))`
`=1.1 xx 10^(-3) ms^(-1)`
(b) (i) The thermal speed of electron of mass m at temperature T is ,
`v=sqrt((3 KT)/(m))` ,
Where k is Boltzmann constant.
Here, `T=300K` ,
`k=1.38 xx10^(-23) J "mole"^(-1) K^(-1)` ,
`m=9.1xx10^(-31) kg`
`:. v=[(3xx(1.38 xx10^(-23))xx 300)/(9.1xx10^(-31))]^(1//2)`
`=1.17xx10^(5) ms^(-1)`
`:. v_(d)/v=1.1xx10^(-3)/1.17xx10^(5)~~10^(-8)`
(ii) The speed of propagation of electric field is equal to the speed to the of an electromagnetic wave,
`c=3xx10^(8)m//s`
`:. (v_d)/(c)=1.1xx10^(-3)/(3xx10^(8))=0.36 xx 10^(-11) =3.6xx10^(-12)`