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. A wire made from zinc with a cross-section of diameter 0.900 mm carries a current of 10.0 A. The "area current density" is 9.824 x10^25. The density of zinc is 7.14 g/cm3, and its atomic mass is 65.4. the number density of free charges in the wire, in electrons/m3 is 1.314 x10^29.Use your results to calculate the drift speed (i.e., the average net speed) of the electrons in the wire.Due to thermal motion, the electrons at room temperature are randomly traveling to and fro at 1.16

Explanation / Answer

Diameter = D = 0.9 mm = 0.9 x 10-3 m

Current = I = 10 A

Current density = Current / Area = I/(0.25*pi*D^2) = 10/(0.25*pi*0.9*10^-3*0.9*10^-3) = 1.572 x 107 A/m^2

Density of zinc = 7.14 g/cm3 = 7140 kg/m^3

Atomic mass of zinc = 65.4

Number density of free charges in the wire = n = 1.314 x 1029 electrons /m^3

Drift speed = J /(n*e)

= (1.572*10^7)/(1.314*10^29*1.6*10^-19)

= 0.000747 m/s

Therefore Drift speed = 0.000747 m/s

Speed due to thermal motion = 1.16 x 10^5 m/s

Fraction = (0.000747/(1.16*10^5)) =6.44 x 10 -9

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