A copper wire of diameter `2/(3sqrtpi)mm` is carrying a current of 1 amp. Calculate the number of free electrons which flow past any cross section of the wire per sec Also find the average speed with which free electrons are flowing in the copper wire assuming that there is one free electron per atom of copper. Number of atmos per `cm^3` of copper `=9 times 10^22`, electronic charge `=1.6 times 10^-19` coulomb.

Explanation

Diameter `d=2/(3sqrtpi)mm=2/(3sqrtpi)times10^-3m`
Area of cross section
`A=1/4pid^2=1/4timespitimes4/(9pi)times10^-6m^2=1/9times10^-6m`
Number density of free electros(n) =number of copper atoms In unit volume
`=9 times 10^22cm^-3=9 times 10^28 m^-3`
Average speed of free electrons through the copper wire
`v=1/(n eA)=1/((9times10^28)times(1.6times10^-19)times(1/9times10^-6))`
`=6.25 times 10^-4.s^-1`
Number of free electrons flowing past any cross section of the wire per unit time
`=nAv=1/e=1/(1.6times10^19)=6.25times10^18s^-1`