A 230 km long high-voltage transmission line 2.0 cm in diameter carries a steady current of 990 A. If the conductor is copper with a free charge density of 8.0*10^28 electrons per cubic meter, how long (in years) does it take one electron to travel the full length of the cable?

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anonymous · Answer

Dividing the current by the Faraday constant, I find that 10.26 mmol/s of electrons are exiting the wire.  Dividing the charge carrier density by Avogadro's number, I find there are 132.84 mmol/cm^3 of free electrons in the wire, so that all the free electrons in 0.0772 cm^3 of the wire must be ejected each second.  Since the wire has a cross sectional area of 12.57 cm^2, this means all the electrons in 0.00615 cm of the wire must be ejected each second.  For an electron just injected at the front of the wire, it would take 230 km/(0.00615 cm/s) = 3.74 x 10^9 s = 119. years to get ejected from the end.

anonymous · Answer

Thank you!!!