Answer:
The separation between the two point charges is decreased by a factor of [tex]4\sqrt{2}[/tex].
Explanation:
By Coulomb's Law, the electric force ([tex]F[/tex]) is inversely proportional to the square of separation ([tex]r[/tex]), that is:
[tex]\frac{F_{2}}{F_{1}} = \frac{r_{1}^{2}}{r_{2}^{2}}[/tex] (1)
If we know that [tex]\frac{F_{2}}{F_{1}} = 32[/tex], then the factor associated with separation between point charges is:
[tex]\frac{r_{1}}{r_{2}} = \sqrt{\frac{F_{2}}{F_{1}} }[/tex]
[tex]\frac{r_{1}}{r_{2}} = \sqrt{32}[/tex]
[tex]\frac{r_{1}}{r_{2}} = 4\sqrt{2}[/tex]
The separation between the two point charges is decreased by a factor of [tex]4\sqrt{2}[/tex].
