What is the average time between collisions for conduction electrons in copper?

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SUMMARY

The average time between collisions (T) for conduction electrons in copper can be computed using the formula T = (Vd)(Me)/(-e)(E), where Vd is the drift velocity, Me is the mass of the electron, and -e is the charge of the electron. In this discussion, a copper wire with a diameter of 1.0 mm carrying a current of 1A is analyzed, yielding a drift velocity (Vd) of 9.4 x 10^-5 m/s. The resistivity of copper is given as 1.72 x 10^-8 ohm·m, which is essential for calculating the electric field (E) and ultimately determining T. The correct approach involves calculating the current density (J) and using it to find the electric field.

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  • Understanding of drift velocity in conductors
  • Familiarity with the properties of copper, including its resistivity
  • Knowledge of basic electrical equations, including Ohm's Law
  • Concept of electron density in materials
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  • Calculate the current density (J) for a copper wire using J = I/A
  • Learn how to derive the electric field (E) from resistivity and current density
  • Explore the relationship between drift velocity (Vd) and electron density (n) in conductors
  • Investigate the impact of temperature on the resistivity of copper
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Homework Statement


compute the average time between collisions T for conduction electrons in copper.


Homework Equations


Vd=-e*E*T/(Me)
Where e is electron's charge
E is electric Field
T is what I'm solving for
And Me is mass of the electron

Vd=I/PA


The Attempt at a Solution



so it was given that a copper wire with a 1.0mm diameter had a current of 1A...and it's mass density is 8900kg/m^3.
So m= 1 electron(8900kg/m^3)(6.02X10^23 atoms/0.0635kg) = 8.4 X 10^28/m^3
So
Vd=1A/(8.4X10^28 m^-3)(1.6X10^-19C)(7.9x10^-7m^2) = 9.4 x 10^-5 m/s

So now...
Vd=-e*E*T/(Me)

So T=(Vd)(Me)/(-e)(E)
I have Vd, Me is mass of the electron, and -e is charge of the electron. I need the electric force...and am stumped. How do I get it from the given info? Thanks for the help.
 
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Current density J = I/A, And resistivity of the material rho = E/J.
E = rho*I/A. For copper rho = 1.72x10^-8ohm.m
Vd = J/nq, where n is electron density in copper = 8.5x10^28 m^-3.
See whether these hints helpful to solve the problem.
 
Ok, so I get E=rho*J.....or since I don't know J J is also Vd*nq...so I get E=rho*Vd*nq...
so my equation becomes T=(Vd)(Me)/(-e)(rho)(Vd)(Nq)
stuff cancels and I get Me/(-e)(rho)(Nq) and I get a really wrong number. hmm
Edit. Nevermind...my bad. We Have I and A can be easily solved giving J. Thanks again, always appreciated.
 

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