Question

How would you change the distance between two charged particles to increase the electric force between them by a factor of 16

Answer 1

The electrostatic force between two charges is inversely
proportional to the square of the distance between them.

So if you want to multiply the force by, say, ' Q ',
you need to multiply the distance by  ( 1 / √Q ) .

We want to multiply the force by 16, so we need to
multiply the distance by    ( 1 / √16 )  =  ( 1 / 4 ) .

The distance should be changed to  1/4  of what it is now.

Answer 2

Reduce the distance by a factor of 4