Question

A charged balloon and a charged piece of fur exert 18.0 N of force on each other. How would you need to change the distance between the two objects so that they exert 2.0 N of force on each other?

Answer 1

We can use Coulomb's law:

$F=k\cdot\frac{|q1||q2|}{r^2}$

Let:

$\begin{gathered} F1=18.0N \\ F2=2.0N \end{gathered}$

So:

$\begin{gathered} F1=k\cdot\frac{|q1||q2|}{r_1^2} \\ F2=k\frac{\lvert q1\rvert\lvert q2\rvert}{r_2^2} \\ \frac{F2}{F1}: \\ \frac{2}{18}=\frac{\frac{k|q1||q2|}{r_2^2}}{\frac{k|q1|q2|}{r_1^2}} \\ \frac{1}{9}=\frac{r_1^2}{r_2^2} \\ so: \\ r_1^2=\frac{1}{9}r_2^2 \end{gathered}$

Therefore, we need to decrease the distance by a factor of 9.