How Long Does an Electron Take to Travel the Length of a High-Voltage Cable?

AI Thread Summary
To determine how long an electron takes to travel the length of a 200-km high-voltage cable carrying a current of 1000 A, one must understand the relationship between current, charge density, and electron drift velocity. The free charge density of copper is given as 8.5 x 10^28 electrons per cubic meter. The relevant equations involve calculating the drift velocity of electrons using the current formula I = ΔQ/Δt and relating it to the charge density. The confusion arises around the interpretation of charge density and its application in the calculations. Ultimately, the solution requires using the charge density to find the drift velocity and then calculating the time taken for an electron to traverse the cable's length.
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Homework Statement


A 200-km-long high-voltage transmission line 2 cm in diameter carries a steady current of 1000 A. If the conductor is copper with a free charge density of 8.5 x 10^28 electrons per cubic meter, how many years does it take one electron to travel th full length of the cable?


The Attempt at a Solution



I know that you need to use this equation: R=p\frac {l}{A} and I think I will also need this equation: I= \frac {\Delta {Q}}{\Delta t}, but I'm not entirely sure.

The thing I most confused about is the "density of 8.5 x 10^28 electrons per cubic meter. Is that a volume? Are you suppose to use: I= \frac {\Delta {Q}}{\Delta t} to find the time (years)?? I'm stuck from here on out. It'd be great if you could give me some hints as to how to continue. Thanks in advance! :smile:
 
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I don't think you need the resistivity equation, just use the charge density equation and the equation for current expressed in terms of charge flux.
 
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