Question

Two small charged spheres are 6.52cm apart. They are moved and the force each exerts on the other is found to have tripled. How far apart are they now?

Answer 1

Coulomb's law is valid not only for point charges, but also for spherical charges. Therefore, the force between charges $q_1$ and $q_2$ can be calculated as (see https://en.wikipedia.org/wiki/Coulomb%27s_law)

$F = k\dfrac{q_1q_2}{r^2},$ where $r$ is the distance between charges.

$r_1=6.52\,\mathrm{cm}, \;\; r_2 - ?$

Let us calculate the ratio of the forces:

$\dfrac{F_2}{F_1} = 3 = \dfrac{ k\dfrac{q_1q_2}{r_2^2}}{ k\dfrac{q_1q_2}{r_1^2}} = \dfrac{r_1^2}{r_2^2}.$

Therefore, $\dfrac{r_1}{r_2} = \sqrt{3}$ and $r_2 = \dfrac{r_1}{\sqrt{3}} = \dfrac{6.52\,\mathrm{cm}}{\sqrt{3}} \approx 3.76\,\mathrm{cm}.$