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(|q1||q2|)/(r^2)`

Let:

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

So:

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

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