The population of the Earth is roughly eight billion people. If all free electrons contained in this extension cord are evenly split among the humans, how many free electrons (NeNeN_e) would each person get? Use two significant figures.

Explanation:

the same question  was in my book hehehe so i am telling this from my book

Drift velocity: 3.32\cdot 10^{-4}m/s

2) 5.6\cdot 10^{13} electrons per person

For a current flowing through a conductor, the drift velocity of the electrons is given by the equation:

v_d=\frac{I}{neA}

where

I is the current

n is the concentration of free electrons

e=1.6\cdot 10^{-19}C is the electron charge

A is the cross-sectional area of the wire

The cross-sectional area can be written as

A=\pi r^2

where r is the radius of the wire. So the equation becomes

In this problem, we have:

I = 8.0 A is the current

is the concentration of free electrons

d = 1.5 mm is the diameter, so the radius is

r = 1.5/2 = 0.75 mm =0.75.10^-3m

Therefore, the drift velocity is:

vd=8.0/(8.5.10^28)(1.6.10^19)π(0.75.10^-3)^2=3.32.10^-4m/s

2)The total length of the cord in this problem is

L = 3.00 m

While the cross-sectional area is

A=π ^2=π (0.75.10^-3)^2=1.77.10^-6m^2

Therefore, the volume of the cord is

V=AL(1)

The number of electrons per unit volume is n, so the total number of electrons in this cord is

N=nV=nAL=(8.5.10^28)(1.77.10^-6)(3.0)=4.5.10^23

In total, the Earth population consists of 8 billion people, which is

N^1=8.10^9

Therefore, the number of electrons that each person would get is:

N^e=N/N^1=4.5.10^23/8.10^9=5.6.10^13

hope it helps

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