A copper bar 1.0 cm x1.0 cm in cross-sectional area and 3.0 m longhas a steady p

Question

A copper bar 1.0 cm x1.0 cm in cross-sectional area and 3.0 m longhas a steady potential of 1.2 V between its two long ends. Find thecurrent flowing through the bar, the current density, and theelectric field strength in the bar.

(a) How many electrons per second flow past any point of thebar?

(b) Assuming there is one free conduction electron available pereach copper atom. Find the average drift velocity of the electronsvd.

(c) How long does it take on average for an electron to flow fromone end to the other end of the bar.

(The atomic weight of copper is 63.5, and the density of copper is8.96 g/cm3. The resistivity of copper is1.7×10-8 •m.)

Explanation / Answer

a) How many electrons per second flow past any point of thebar?
Since Voltage drom V in terms of resistance R and current Iis V=IR I= V/R where resistance R in terms of resistivity, crossectional area A and length L is R= L/A I=nq/t then electrons per second n/t is Finally n/t= V/(Rq) = VA/(qL) =1.7×10-8 •m n/t = 1.2 x 0.01x0.01 /(1.602x10-19 x1.7×10-8 x 3.0) n/t = 1.47 x1022 electrons/sec (b) Assuming there is one free conduction electron availableper each copper atom. Find the average drift velocity of theelectrons vd.
vd = I/(nqA) from earlier I=V/R we have vd = V/(nqAR) since R=L/A vd = V/(nq L) since = 8.96 g/cm3 for copper ; Avogadro's number N =6.0221415 × 1023atoms/mol n= N /(gram/mole V)  =N / (gram/mole LA) now vd = V /(NqL / (gram/mole LA)) vd = V (gram/mole A)/(N q ) =1.7×10-8 •m vd = V/(nq L) since = 8.96 g/cm3 for copper ; Avogadro's number N =6.0221415 × 1023atoms/mol n= N /(gram/mole V)  =N / (gram/mole LA) now vd = V /(NqL / (gram/mole LA)) vd = V (gram/mole A)/(N q ) =1.7×10-8 •m vd = 1.2 (63.5 x8.96 x103 x 0.01x0.01) / (6.0221415 × 1023 x1.602x10-19 x1.7×10-8 ) vd = 41,630 m/s
(c) How long does it take on average for an electron to flow fromone end to the other end of the bar.
t= L/vd = t=3.0 / 41,630 = t= 72 x10 -6 s (The atomic weight of copper is 63.5, and the density ofcopper is 8.96 g/cm3. The resistivity of copper is1.7×10-8 •m.)

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