To solve this problem we will apply the concepts related to the average velocity in an electron, defined as the value of the current on the product between the charge, the number of electrons, the constancy pi and the squared radius. Our values are given as,
[tex]D = 2.05 mm[/tex]
[tex]I = 5A[/tex]
[tex]e = -1.6 x 10^{-19} C[/tex]
[tex]Q = 10^{23} e/cm^3 = 10^{29}e/m^3[/tex]
The radius would b,
[tex]R = \frac{D}{2} = \frac{2.05*10^{-3}m}{2}[/tex]
[tex]R = 1.025*10^{-3}m[/tex]
Now the average velocity
[tex]V = \frac{I}{(Q e \pi R^2)}[/tex]
Here,
I = Current
Q = Electron concentration
e = Charge of electron
R = Radius
[tex]V = \frac{5}{(10^{29})(-1.6*10^{-19})(\pi)(1.025*10^{-3})^2}}[/tex]
[tex]V = 9.46*10^{-5}m/s[/tex]
Converting to the values required we have that,
[tex]V = 9.46*10^{-5} m/s (\frac{1000mm}{1m})[/tex]
[tex]V = 9.46*10^{-2}mm/s[/tex]
And,
[tex]V = 9.46*10^{-5}m/s (\frac{3600s}{1hour})(\frac{0.000621371miles}{1m})[/tex]
[tex]V = 2.116*10^{-4}mph[/tex]
