The point of this problem is to show how slowly electrons travel on average thro

Question

The point of this problem is to show how slowly electrons travel on average through a thin wire, even for large values of current.

1) A wire made from copper with a cross-section of diameter 0.940 mm carries a current of 13.0 A. Calculate the "areal current density"; in other words, how many electrons per square meter per second flow through this wire? (Enter your answer without units.)

2) The density of copper is 8.90 g/cm3, and its atomic mass is 63.5. Assuming each copper atom contributes one mobile electron to the metal, what is the number density of free charges in the wire, in electrons/m3? (Enter your answer without units.)

3) Use your results to calculate the drift speed (i.e., the average net speed) of the electrons in the wire.

4) Due to thermal motion, the electrons at room temperature are randomly traveling to and fro at 1.15×105 m/s, even without any current. What fraction is the current's drift speed, compared to the random thermal motion?

Explanation / Answer

1) Current density, J = I/A

= I/(pi*d^2/4)

= 13/(pi*(0.94*10^-3)^2/4)

= 1.87*10^7 A/m^2

= 1.87*10^7 (C/s)/m^2

= 1.87*10^7/(1.6*10^-19) (electrons/s)/m^2

= 1.17*10^26 (electrons/s)/m^2

2) density of copper = 8900 kg/m^3

mass of one copper atom, m = 63.5*1.66*10^-27 kg

= 1.0541*10^-25 kg

no aotms that exist in 8900 kg, N = 8900/(1.0541*10^-25)

= 8.44*10^28 atoms

no of electrons per meter cube, n = 8.44*10^28 electrons/m^3

3) drift speed, vd = J/n

= 1.17*10^26/(8.44*10^28)

= 1.38*10^-3 m/s

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