1) Drift velocity: ![3.32\cdot 10^{-4}m/s](https://tex.z-dn.net/?f=3.32%5Ccdot%2010%5E%7B-4%7Dm%2Fs)
2)
electrons per person
Explanation:
1)
For a current flowing through a conductor, the drift velocity of the electrons is given by the equation:
![v_d=\frac{I}{neA}](https://tex.z-dn.net/?f=v_d%3D%5Cfrac%7BI%7D%7BneA%7D)
where
I is the current
n is the concentration of free electrons
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](https://tex.z-dn.net/?f=A%3D%5Cpi%20r%5E2)
where r is the radius of the wire. So the equation becomes
![v_d=\frac{I}{ne\pi r^2}](https://tex.z-dn.net/?f=v_d%3D%5Cfrac%7BI%7D%7Bne%5Cpi%20r%5E2%7D)
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\cdot 10^{-3}m](https://tex.z-dn.net/?f=0.75%5Ccdot%2010%5E%7B-3%7Dm)
Therefore, the drift velocity is:
![v_d=\frac{8.0}{(8.5\cdot 10^{28})(1.6\cdot 10^{-19})\pi(0.75\cdot 10^{-3})^2}=3.32\cdot 10^{-4}m/s](https://tex.z-dn.net/?f=v_d%3D%5Cfrac%7B8.0%7D%7B%288.5%5Ccdot%2010%5E%7B28%7D%29%281.6%5Ccdot%2010%5E%7B-19%7D%29%5Cpi%280.75%5Ccdot%2010%5E%7B-3%7D%29%5E2%7D%3D3.32%5Ccdot%2010%5E%7B-4%7Dm%2Fs)
2)
The total length of the cord in this problem is
L = 3.00 m
While the cross-sectional area is
![A=\pi r^2=\pi (0.75\cdot 10^{-3})^2=1.77\cdot 10^{-6} m^2](https://tex.z-dn.net/?f=A%3D%5Cpi%20r%5E2%3D%5Cpi%20%280.75%5Ccdot%2010%5E%7B-3%7D%29%5E2%3D1.77%5Ccdot%2010%5E%7B-6%7D%20m%5E2)
Therefore, the volume of the cord is
(1)
The number of electrons per unit volume is
, so the total number of electrons in this cord is
![N=nV=nAL=(8.5\cdot 10^{28})(1.77\cdot 10^{-6})(3.0)=4.5\cdot 10^{23}](https://tex.z-dn.net/?f=N%3DnV%3DnAL%3D%288.5%5Ccdot%2010%5E%7B28%7D%29%281.77%5Ccdot%2010%5E%7B-6%7D%29%283.0%29%3D4.5%5Ccdot%2010%5E%7B23%7D)
In total, the Earth population consists of 8 billion people, which is
![N'=8\cdot 10^9](https://tex.z-dn.net/?f=N%27%3D8%5Ccdot%2010%5E9)
Therefore, the number of electrons that each person would get is:
![N_e = \frac{N}{N'}=\frac{4.5\cdot 10^{23}}{8\cdot 10^9}=5.6\cdot 10^{13}](https://tex.z-dn.net/?f=N_e%20%3D%20%5Cfrac%7BN%7D%7BN%27%7D%3D%5Cfrac%7B4.5%5Ccdot%2010%5E%7B23%7D%7D%7B8%5Ccdot%2010%5E9%7D%3D5.6%5Ccdot%2010%5E%7B13%7D)