a) A wire made from zinc with a cross-section of diameter 0.810 mm carries a cur
ID: 1778708 • Letter: A
Question
a) A wire made from zinc with a cross-section of diameter 0.810 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 zinc is 7.14 g/cm3, and its atomic mass is 65.8. Assuming each zinc atom contributes two 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 1.13×105 m/s, even without any current. What fraction is the current's drift speed, compared to the random thermal motion?
Explanation / Answer
a)
A = area of cross-section = (0.25) pi d2 = (0.25) (3.14) (0.81 x 10-3)2 = 5.2 x 10-7 m
i = current = 10 A
current density is given as
J = I/A = 10/(5.2 x 10-7) = 1.92 x 107 A/m2
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