Question

Two charged particles are 8.45 cm apart. They are moved and the force on 

each of them is found to have tripled. How far are they now?

Answer 1

The force between two charges can be written as follows:

$$F=\dfrac{kq_1q_2}{r^2}.$$

If the force is tripled we get the next formula:

$$3F=\dfrac{kq_1q_2}{r_{new}^2}.$$

Let's divide second equation by first equation:

$$\dfrac{3F}{F}=\dfrac{r^2}{r_{new}^2},$$ $$r_{new}=\sqrt{\dfrac{r^2}{3}}=\sqrt{\dfrac{(8.45\ cm)^2}{3}}=4.88\ cm.$$