Question

Two point charges are brought closer together, increasing the force between them by a factor of 32. By what factor was their separation decreased

Answer 1

Answer:

The separation between the two point charges is decreased by a factor of $4\sqrt{2}$.

Explanation:

By Coulomb's Law, the electric force ($F$) is inversely proportional to the square of separation ($r$), that is:

$\frac{F_{2}}{F_{1}} = \frac{r_{1}^{2}}{r_{2}^{2}}$ (1)

If we know that $\frac{F_{2}}{F_{1}} = 32$, then the factor associated with separation between point charges is:

$\frac{r_{1}}{r_{2}} = \sqrt{\frac{F_{2}}{F_{1}} }$

$\frac{r_{1}}{r_{2}} = \sqrt{32}$

$\frac{r_{1}}{r_{2}} = 4\sqrt{2}$

The separation between the two point charges is decreased by a factor of $4\sqrt{2}$.