Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area `3.0 xx 10^(-7) m^(2)` carrying a current of 5A. Assume that each copper atom contributions 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.

Explanation

Given corss-sectional area of copper wire, `A = 3 xx 10^(-7) m^(2)`
carrying current of copper, I = 5A
charge of electron, `e = 1.6 xx 10^(-19) C`
Density of conduction electrons = No. of atoms per cubic meter,
`n = (N_(A) ("Avogadro number") xx "mass of copper" (M) "per cubic meter")/("Atomic mass"(m))`
`:. n = (6 xx 10^(23) xx 9 xx 10^(3))/(63.5) = 8.5 xx 0^(23) m^(-3)`
`:.` Average drift speed of conduction electrons.
`V_(d) = (I)/(neA) = (5)/(8.5 xx 10^(28) xx 1.6 xx 10^(-19) xxx 3 xx 10^(-7))`
`implies V_(d) = (5)/(8.5 xx 1.6 xx 3 xx 10^(2)) = 0.1225 xx 10^(-2) m//s`
`:. V_(d) = 1.225 mm//s`