# Homework Help: E-Field Through Copper Wire given drift velocity

1. Nov 1, 2016

### stephen8686

1. The problem statement, all variables and given/known data
If the magnitude of the drift velocity of free electrons in a copper wire is 7.84×10-4 m/s, what is the electric field in the conductor? (Also gives chart that states that the resistivity of Cu is 1.7×10-8 Ωm)

2. Relevant equations

vd=(qEτ)/me (where τ is avg. time between collisions)

ρ=1/σ=me/(nq2τ)

3. The attempt at a solution

first I solved for τ in the second equation:
τ=me/(nq2ρ)

Then I put this value in for τ in the first equation:
vd=(qE(me/(nq2ρ))/me
Simplify:
vd=E/(qnp)

When I put in values:
7.84×10-4=E/(1.6×10-19)(1.7×10-8)(n)
I didn't know how to get n (number of e- per m3), so I googled the density of copper (8.96 g/ml) and did some conversions to get n=8.475×1028, which gave me a correct answer of E=.18V/m, but I don't think I was supposed to use google, and no density chart is given in the book. Is there another way to do this that I overlooked?

2. Nov 2, 2016

### kuruman

There is a more direct way that does not involve τ. The current density is related to the electric field by J = (1/ρ) E and to the drift velocity by J = n e vd. You still need n which you cannot get from what is given unless you look things up.

3. Nov 2, 2016

### stephen8686

Thanks kuruman. Just wanted to make sure I wasn't missing anything important.