Average Electron Drift Distance with AC Current

[achap6]

Homework Statement

A metal wire with 10²³ free electrons per cubic centimeter is carrying 60 Hz alternating current with a maximum current density of 100 amps/cm².
a) Write an expression for the average electron drift velocity as a function of time (v_d as a function of time).
b) What is the average drift distance of free electrons in one direction in a half-cycle of current?

Homework Equations

J = σE = σEsin(ωt)
ω = 2πν
J = -eN_ev_d

The Attempt at a Solution

Part a:

J = -eN_ev_d
-eN_ev_d = σEsin(ωt)
v_d = (-σEsin(ωt)) / (eN_e)

Part b:

Need help here, I attempted to plug in ω = 2πν into the equation J = σEsin(ωt), but don't seem to be getting anywhere, because I don't have σ or E.

 

[Hesch]

A metal wire with 10²³ free electrons per cubic centimeter is carrying 60 Hz alternating current with a maximum current density of 100 amps/cm^2.

Calculate the average absolute current density ( [ A/cm² ] ).

Calculate the amount of coulombs moved per second.

Calculate the amount of centimeter wire-electrons is moved per second.