Extra 17.5.01 The density of mobile electrons in copper metal is 8.4 x 10m Suppo

Question

Extra 17.5.01 The density of mobile electrons in copper metal is 8.4 x 10m Suppose thati 64 10electrons/s are drifting through a copper wire. (This is a typical value for a simple circuit.) The diameter of the wire is 1.5mm. In this case, about how many minutes would it take for a single electron in the electron sea to drift from one end to the other end of a wire 36 cm leng? minutes (Apuzzle:the drit speed is so slow, how can a lamp ight up as soon as you turn it on? we" come back to this in the next me number of signikant digits is set to 3; the tolerance is +/-2% apter)

Explanation / Answer

drift velocity Q / t = n q vd A

A = pi * (0.75 * 10-3)2 = 1.77 * 10-6 m2

Q/t = 6.4 * 1018 * 1.6 * 10-19 = 1.024 C/s

Q / t = n q vd A

1.024 = 8.4 * 1028 * 1.6 * 10-19 * vd * 1.77 * 10-6

vd = 4.3 * 10-5 m/s

d = v t

t = d / v = 0.36 / 4.3 * 10-5

required time = 8363 sec = 139.4 min

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