A 310-km-long high-voltage transmission line 2.00 cm in diameter carries a steady current of 1,010 A. If the conductor is copper with a free charge density of 8.50 1028 electrons per cubic meter, how many years does it take one electron to travel the full length of the cable? (Use 3.156 107 for the number of seconds in a year.)

In order to calculate the amount of years that electrons take to cross the complete transmission line. You first calculate the drift speed of the electrons by using the following formula:

[tex]v_d=\frac{I}{nqA}[/tex] (1)

I: current on the wire = 1,010A

n: free charge density = 8.50*10^28 electrons/m^3

A: cross-sectional area of the transmission line = π*r^2

r: radius of the cross-sectional area = 2.00cm = 0.02m

You replace the values of the parameters in the equation (1):

[tex]v_d=\frac{1,010A}{(8.50*10^{28}electron/m^3)(1.6*10^{-19}C)(\pi (0.02m)^2)}\\\\v_d=5.9*10^{-5}\frac{m}{s}[/tex]

Next, you use the following formula:

[tex]t=\frac{x}{v_d}[/tex] (2)

x: length of the line transmission = 310km = 310,000m

You replace the values of vd and x in the equation (2):

[tex]t=\frac{310,000m}{5.9*10^{-5}m/s}=5.24*10^9s[/tex]

Finally, you convert the obtained t to seconds

[tex]t=5.24*10^9s*\frac{1\ year}{3.156*10^7s}=166.03\ years[/tex]

The electrons take approximately 166 years to travel trough the complete transmission line