What happens to the force between two charges if the distance between them is quadrupled?

The new force between the two objects will be 1/16 of what the original force was.

This relationship can be found by using this equation:

In this case "r" represents the distance between the two charges, the "Q"s represent the two charges, the "k" represents Coulomb's constant, and "F" is the force.

Since "r" increased by a factor of 4 in the problem, and (4r)2 equals 16r2, then the "new" Force (Fn) is proportional to 1/16r2. You can use proportionality to set up the equation 16Fn = Fo where Fn is the new force and Fo is the original force. If you divide both sides by 16 to solve for Fn, you come up with the fact that the "new" force equals the original force over 16, which demonstrates that the "new" force is 1/16 of the original.