Answer:
The force becomes 4 times as much when the distance is halved.
Explanation:
F1 = k*q1 * q2/r^2 = kq^2/r^2
F2 = kq^2/1 / (r/2)^2
Set up a proportion using F1/F2 as you reference.
Notice that you don't know any number that can be used in this equation. However k q^2 does not change as you move the two charges closer together. That being so, you can still show what happens to F1 and F2.
F1/F2 = 1/r^2 // 1/(r^2/4)
Take the denominator, invert the fraction and multiply. That creates another cancellation.
F1/F2 = 1/r^2 * r^2 /4 1
F1/F2 = r^2 // r^2/4 which allows you to cancel r^2
F1/F2 = 1/4 Now you need to interpret F1 and F2. Cross Multiply
4F1 = F2
