A) 16.1 N
The magnitude of the electric force between the corks is given by Coulomb's law:
[tex]F=k\frac{q_1 q_2}{r^2}[/tex]
where
k is the Coulomb's constant
[tex]q_1 = 6.0 \mu C=6.0 \cdot 10^{-6} C[/tex] is the magnitude of the charge on the first cork
[tex]q_2 = 4.3 \mu C = 4.3 \cdot 10^{-6}C[/tex] is the magnitude of the charge of the second cork
r = 0.12 m is the separation between the two corks
Substituting numbers into the formula, we find
[tex]F=(9\cdot 10^9 N m^2 C^{-2} )\frac{(6.0\cdot 10^{-6}C)(4.3\cdot 10^{-6} C)}{(0.12 m)^2}=16.1 N[/tex]
B) Attractive
According to Coulomb's law, the direction of the electric force between two charged objects depends on the sign of the charge of the two objects.
In particular, we have:
- if the two objects have charges with same sign (e.g. positive-positive or negative-negative), the force is repulsive
- if the two objects have charges with opposite sign (e.g. positive-negative), the force is attractive
In this problem, we have
Cork 1 has a positive charge
Cork 2 has a negative charge
So, the force between them is attractive.
C) [tex]2.69\cdot 10^{13}[/tex]
The net charge of the negative cork is
[tex]q_2 = -4.3 \cdot 10^{-6}C[/tex]
We know that the charge of a single electron is
[tex]e=-1.6\cdot 10^{-19}C[/tex]
The net charge on the negative cork is due to the presence of N excess electrons, so we can write
[tex]q_2 = Ne[/tex]
and solving for N, we find the number of excess electrons:
[tex]N=\frac{q_2}{e}=\frac{-4.3\cdot 10^{-6} C}{-1.6\cdot 10^{-19} C}=2.69\cdot 10^{13}[/tex]
D) [tex]3.75\cdot 10^{13}[/tex]
The net charge on the positive cork is
[tex]q_1 = +6.0\cdot 10^{-6}C[/tex]
We know that the charge of a single electron is
[tex]e=-1.6\cdot 10^{-19}C[/tex]
The net charge on the positive cork is due to the "absence" of N excess electrons, so we can write
[tex]q_1 = -Ne[/tex]
and solving for N, we find the number of electrons lost by the cork:
[tex]N=-\frac{q_1}{e}=-\frac{+6.0\cdot 10^{-6} C}{-1.6\cdot 10^{-19} C}=3.75\cdot 10^{13}[/tex]
