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

The separation between the two point charges is decreased by a factor of
`4√(2)`.

Step-by-step explanation:

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

`(F_(2))/(F_(1)) = (r_(1)^(2))/(r_(2)^(2))` (1)

If we know that
`(F_(2))/(F_(1)) = 32`, then the factor associated with separation between point charges is:

`(r_(1))/(r_(2)) = \sqrt{(F_(2))/(F_(1)) }`

`(r_(1))/(r_(2)) = √(32)`

`(r_(1))/(r_(2)) = 4√(2)`

The separation between the two point charges is decreased by a factor of
`4√(2)`.