2.0 3 102 - km - long high - voltage transmission line 2.0 cm in diameter carries a steady current of 1.0 3 103 A. If the conductor is copper with a free charge density of 8.5 3 1028 electrons/m3, how many years does it take one electron to travel the full length of the cable?

21.2 years

Explanation:

Length, L = 2.03 x 10^2 km = 2.03 x 10^5 m

Diameter, d = 2 cm

radius, r = 1 cm = 0.01 m

Current, i = 1.03 x 10^3 A

charge density, n = 8.53 x 10^28 electrons/m^3

Let the time taken by the electrons be t.

By the use of the formula for the drift velocity

i = n e A vd

where, e be the electronic charge, A be the area of crossecion and vd be the drift velocity

1.03 x 10^3 = 8.53 x 10^28 x 1.6 x 10^-19 x 3.14 x 0.01 x 0.01 x vd

vd = 3.033 x 10^-4 m/s

time taken, t = length / drift velocity

t = 2.03 x 10^5 / (3.033 x 10^-4)

t = 6.69 x 10^5 seconds

t = 21.2 years

Thus, the time taken is 21.2 years.