The time taken by an electron to travel the length of the line is required.
The time taken is 50.4 years.
Drift velocity
I = Current = [tex]1.08\times 10^{3}\ \text{A}[/tex]
d = Diameter of wire = 2.4 cm
r = Radius of wire = d/2 = 2.4/2 = 1.2 cm = 0.012 m
n = Free charge density of copper = [tex]8.46\times 10^{28}\ \text{electrons/m}^3[/tex]
e = Magnitude of charge of electron = [tex]1.6\times 10^{-19}\ \text{C}[/tex]
A = Area = [tex]\pi r^2[/tex]
[tex]v_d[/tex] = Drift velocity
L = Length of wire = 280 km = 280000 m
Current is given by
[tex]I=neAv_d\\\Rightarrow v_d=\dfrac{I}{neA}\\\Rightarrow v_d=\dfrac{1.08\times 10^3}{8.46\times 10^{28}\times 1.6\times 10^{-19}\times \pi 0.012^2}\\\Rightarrow v_d=1.76\times 10^{-4}\ \text{m/s}[/tex]
Time is given by distance divided by speed, so
[tex]t=\dfrac{L}{v_d}\\\Rightarrow t=\dfrac{280000}{1.76\times 10^{-4}}\\\Rightarrow t=1.59\times 10^9\ \text{s}[/tex]
Converting to years
[tex]\dfrac{1.59\times 10^{9}}{365.25\times 24\times 60\times 60}=50.4\ \text{years}[/tex]
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