Question The point of this problem is to show how slowly electrons travel on ave

Question

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 0.730 mm carries a current of 12.0 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.) Tries 0/16 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.) Tries 0/16 Use your results to calculate the drift speed (i.e., the average net speed) of the electrons in the wire. Tries 0/16 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

What a lovely problem. I applaud the creator and thank the person who assigned it.

How far have you gotten on the problem? There are four parts; parts 1 & 2 are completely independent. Did you have problems with both parts or did you not even try?

Part 1 has to do with the definition of current. One ampere is one Coulomb per second, with a Coulomb being 6 241 509 479 607 717 888 elementary charges (in this case electrons)

Since the wire is circular and you have the diameter, you can compute the cross-sectional area and hence the number of electrons per square meter per second.

Part 2 has to do with the density of free electrons in the material. You are give the weight of each atom of iron in atomic mass units:

and the total weight of 1 cc of iron so you can compute the number of atoms per cc. Multiply by two to get the number of free electrons per cc.

Part 3 wants the mean net speed of the mobile electrons. If the net flow is N/second and there are D electrons per unit volume (cc) of material, then there are N/D units of volume have to pass each point in one second. You have the cross-sectional area of the wire, so you can compute the length of wire that would have N/D units of volume. That length has to be traversed in one second. velocity = distance/time.

Part 4 asks you to compare this result with mean thermal speed, which is given.

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.