Two point charges are brought closer together,....

Question

Two point charges are brought closer together, increasing the force between them by a factor of 84. By what factor was their separation decreased?

Answer 1

The force between two charges is inversely proportional to the distance squared. 

 

F=kq₁q₂/r²

 

So if the distance is half, then the force increases by a factor of 4. If the distance is 1/4, the force increases by a factor of 16. Thus, if the force increased by a factor if 84, then the distance has to be 1/sqrt(84) or decreased by a factor sqrt(84) which equals 9.17