A 240-km-long high-voltage transmission line 2.00 cm in diameter carries a steady current of 1,250 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.)

Sure, here's how you can solve this problem:

Step 1: Calculate the volume of the copper wire. The volume (V) of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height (or length in this case). The radius is half the diameter, so r = 1 cm = 0.01 m. The length of the wire is 240 km = 240,000 m. So, the volume of the wire is V = π*(0.01 m)²*(240,000 m) = 75.4 m³.

Step 2: Calculate the total number of electrons in the wire. The total number of electrons (N) is given by the product of the volume and the free charge density (ρ), so N = V*ρ = 75.4 m³ * 8.50 * 10^28 electrons/m³ = 6.41 * 10^30 electrons.

Step 3: Calculate the time it takes for one electron to travel the length of the wire. The current (I) is the rate of flow of charge, given by the formula I = Q/t, where Q is the charge and t is the time. The charge of one electron (Q) is the product of the number of electrons and the charge of one electron, so Q = N*e = 6.41 * 10^30 electrons * 1.6 * 10^-19 C/electron = 1.03 * 10^12 C. Solving the formula for time gives t = Q/I = 1.03 * 10^12 C / 1250 A = 8.24 * 10^8 s.

Step 4: Convert the time from seconds to years. Use the given conversion factor of 3.156 * 10^7 s/year to convert the time to years: t = 8.24 * 10^8 s * (1 year / 3.156 * 10^7 s) = 26.1 years.

So, it takes approximately 26.1 years for one electron to travel the full length of the cable.