# Current density and drift velocity

## Homework Statement

1. A copper wire 2 mm in diameter carries a 4 A current. Determine the current density in the wire, drift velocity of the electrons and the mean time between collisions. Assume that each copper atom contributes one free electron. Hint: you may need some additional parameters of copper to solve this problem.

## Homework Equations

A) For current density: J = I/A
We know: A = ∏r2 m2

B) Drift velocity: I = nqVdA . thus Vd = I / (nqA)
We know: n = density/mass atom, or (8.95g/cm3 X 106 cm3/m3) / 1.05565 X 10-22g/atom = 8.478 X 1028 atoms/m3
q = 1.602 X 10-19 C

C) σ = (nqτ2)/me, thus τ = σme / nq2
and σ = 1/p, p being resistivity, and resistivity for copper is 1.7 X 10-8 ohm*m

## The Attempt at a Solution

A) ∏*0.0022m2 = 1.2265 X 10-5 m2
4 / 1.2265 X 10-5 = 318,309.89 A

B) Simply plug in the numbers: Vd = 4A / (8.478 X 1028/m3 * 1.602 X 10-19 C * 1.2265 X 10-5 m2 = 2.4012 X 10 -5 m/s

C) For C, I have no clue in which direction to go, I've browsed through my book but can't find any relevant formula

Any help for letter C would be appreciated, and also if you can check if what I did in A and B makes sense? Thank you!

Edit: I found something in the book, would the formula on C make sense?

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