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8 April, 21:13

A straight section of silver wire has a cross sectional area A=2.0 mm2. A total of 9.4*1018 electrons pass through the wire in 3.0s. The conduction electron density in silver is 5.8*1028 electrons/m3. How far along the straight section do the electrons in the wire move, on average, during the 3.0s in question?

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  1. 8 April, 22:19
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    8.08 x 10^-5 m

    Explanation:

    A = 2 mm^2 = 2 x 10^-6 m^2

    Total number of electrons, N = 9.4 x 10^18

    time, t = 3 s

    n = 5.8 x 10^28 electrons / m^3

    Current, i = Q / t = N x e / t = (9.4 x 10^18 x 1.6 x 10^-19) / 3 = 0.5 A

    Let vd be the drift velocity.

    i = n e A vd

    0.5 = 5.8 x 10^28 x 1.6 x 10^-19 x 2 x 10^-6 x vd

    vd = 2.7 x 10^-5 m/s

    Distance traveled by the electrons = velocity x time

    = vd x t = 2.7 x 10^-5 x 3 = 8.08 x 10^-5 m
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