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Parad0x88

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## 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 = ∏r

^{2}m

^{2}

B) Drift velocity: I = nqV

_{d}A . thus V

_{d}= I / (nqA)

We know: n = density/mass atom, or (8.95g/cm

^{3}X 10

^{6}cm

^{3}/m

^{3}) / 1.05565 X 10

^{-22}g/atom = 8.478 X 10

^{28}atoms/m

^{3}

q = 1.602 X 10

^{-19}C

C) σ = (nqτ

^{2})/m

^{e}, thus τ = σm

_{e}/ nq

^{2}

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) ∏*0.002

^{2}m

^{2}= 1.2265 X 10

^{-5}m

^{2}

4 / 1.2265 X 10

^{-5}= 318,309.89 A

B) Simply plug in the numbers: V

_{d}= 4A / (8.478 X 10

^{28}/m

^{3}* 1.602 X 10

^{-19}C * 1.2265 X 10

^{-5}m

^{2}= 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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