(a) Esttimate the average drift speed of conduction electrons in a copper wite of cross-secttonal area `1.0 xx 10 ^(-7)m^(2)` carrying a current of `1.5A.` Assume the each copper atom contrbutes 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.` (b) Compare the drift speed obyained above with, (1) thermal speeds of copper atoms at ordinary temperaturtes. (ii) speed of propagation of electric field along the conductor which causes the drift motion.

Explanation

(a)`e=1.6xx10^(-19)C,A=1.0xx10^(-7)m^(2),I=1.5.`
`V_(d)=((I)/("ne"A))`
A cubic meter of copperhas a mass of `9.0xx10^(3)kg`.Since `6.0xx10^(23)` copper atoms have
a mass of 63.5kg,the number kdensity is `n=(6.0xx10^(23))/(63.5)xx9.0xx10^(6)=8.5xx10^(28)m^(-3)`
`V_(d)=(1.5)/(8.5xx10^(28)xx1.6xx10^-(19)xx1.0xx10^(-7))=1.1xx10^(-3)ms^(-1)=1.1mms^(-1)`
(b) (i) We have `[((1)/(2))mv^(2)=((3)/(2))K_(B)T],V=sqrt((3k_(B)T)/m)` m where `k_(B)`is the Boltzmann constant.
For copper at 300 K, this is about `2 xx10^(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 is set up along the conductor has a speed of an electromagnetic wave (equal to `3.0xx10^(8)ms^(-1)`). So drift speed is very small by a factor of `10^(-11)`