Question

Bonnie is dusting the house and raises a cloud of dust particles as she wipes across a table. If two 3.5 x 10-14C pieces of dust exert an electrostatic force of 4.1 x 10-12N on each other, how far apart are the dust particles at that time?

Answer 1

The electrostatic force between the two dust particles is given by:
$F=k \frac{q_1 q_2}{r^2}$
where
$k=8.99 \cdot 10^9 Nm^2C^{-2}$ is the Coulomb constant
$q_1=q_2=q=3.5 \cdot 10^{-14} C$ is the charge of the two particles
$r$ is the separation between the two particles

Since we know the magnitude of the force, we can re-arrange the previous formula to find the separation between the two particles:
$r= \sqrt{ \frac{q^2 k}{F} }= \sqrt{ \frac{(3.5 \cdot 10^{-14} C)^2(8.99 \cdot 10^9 Nm^2C^{-2})}{4.1 \cdot 10^{-12} N} }=1.64 \cdot 10^{-3} m = 1.64 mm$