A copper wire of length 2.0 m, of cross-sectional area 2.0 mm square carries a current of 0.4A. It is assumed that there is only one electron per atom. Atomic mass of copper is 63 g and density of copper is `8.9g//c`. Find the drift velocity for the electrons in the wire. Also find the mobility of electrons if a pot. difference of 100 V is applied across this wire.

Explanation

Here,`l=2.0 m` ,
`A=2.0 mm sq =2.0xx2.0xx10^(-6)m^(2)`,
`I=4.0 A, M=63xx10^(-3)kg`,
density, `rho = 8.9xx10^(3)kg//m^(3), V=100 V`
No. of atoms per unit volume,
`= ("Avogadro's number" xx "density")/("Atomic masss")`
`= (6.023 xx10^(23)xx8.9xx10^(3))/(63xx10^(-3)) =8.5xx10^(28)`
Since one atom contribute only one electron, so number of electron per unit volume is
`n=8.5xx10^(28)m^(-3)`
Drift velocity, `v_(d)=I/nAe`
`4.0/((8.5xx10^(28))(2.0 xx 2.0 xx10^(-6)) (1.6xx10^(-19)))`
`=7.35 xx10^(-5) ms^(-1)`
Mobility of electron, `mu =v_(d)/E =v_(d)/(V//l) = (v_(d) l)/(V)`
`((7.35xx10^(-5))xx2.0)/100`
`=1.47 xx10^(-6) m^(2) V^(-1)s^(-1)`