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) A wire made from aluminum with a cross-section of diameter 0.960 mm carries a current of 10.0 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.)

(B) The density of aluminum is 2.80 g/cm3, and its atomic mass is 27.5. Assuming each aluminum atom contributes three mobile electrons to the metal, what is the number density of free charges in the wire, in electrons/m3? (Enter your answer without units.)

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

(D) Due to thermal motion, the electrons at room temperature are randomly traveling to and fro at 1.16×105 m/s, even without any current. What fraction is the current's drift speed, compared to the random thermal motion?

Explanation / Answer

(a) 10.0A means 10.0 C of charge per second passing a given point. This corresponds to 10/1.60x10^-19 = 6.25x10^19 electrons per second

r=0.960/2=0.48

Or an electron density of 6.25x10^19/(*(0.48x10^-3)^2) =8.63x10^26 electron per m^2 per second

(b) There are 2.80g/cm^3/27.5g/mol*6.022x10^23molecule... electron/molecule
= 1.69x10^23 electron/cm^3 = 1.69x10^29 electrons/m^3

C) vd = J/(n*q) = 10.0/(*(0.48x10^-3)^2)/(1.68x10^29*1.6... = 5.103x10^-3m/s

D) we have 5.103x10^-3m/s /1.16x10^5 =4.404x10^-9

there may be calculation error but concept is right

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