Question

A small cork with an excess charge of +6.0µC is placed 0.12 m from another cork, which carries a charge of -4.3µC.

Answer 1

A) 16.1 N

The magnitude of the electric force between the corks is given by Coulomb's law:

$F=k\frac{q_1 q_2}{r^2}$

where

k is the Coulomb's constant

$q_1 = 6.0 \mu C=6.0 \cdot 10^{-6} C$ is the magnitude of the charge on the first cork

$q_2 = 4.3 \mu C = 4.3 \cdot 10^{-6}C$ 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

$F=(9\cdot 10^9 N m^2 C^{-2} )\frac{(6.0\cdot 10^{-6}C)(4.3\cdot 10^{-6} C)}{(0.12 m)^2}=16.1 N$

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) $2.69\cdot 10^{13}$

The net charge of the negative cork is

$q_2 = -4.3 \cdot 10^{-6}C$

We know that the charge of a single electron is

$e=-1.6\cdot 10^{-19}C$

The net charge on the negative cork is due to the presence of N excess electrons, so we can write

$q_2 = Ne$

and solving for N, we find the number of excess electrons:

$N=\frac{q_2}{e}=\frac{-4.3\cdot 10^{-6} C}{-1.6\cdot 10^{-19} C}=2.69\cdot 10^{13}$

D) $3.75\cdot 10^{13}$

The net charge on the positive cork is

$q_1 = +6.0\cdot 10^{-6}C$

We know that the charge of a single electron is

$e=-1.6\cdot 10^{-19}C$

The net charge on the positive cork is due to the "absence" of N excess electrons, so we can write

$q_1 = -Ne$

and solving for N, we find the number of electrons lost by the cork:

$N=-\frac{q_1}{e}=-\frac{+6.0\cdot 10^{-6} C}{-1.6\cdot 10^{-19} C}=3.75\cdot 10^{13}$