Physics, Two charged particles repel each other with a force F. If the charge of one of the particles is....

Two charged particles repel each other with a force F. If the charge of one of the particles is doubled and the distance between them is also doubled, then the force will be
A) F.
B) 2 F.
C) F/2.
D) F/4.
E) none of these

Please, explain in detail

Thank you

the equation for the force between two charges is

F = K Q1 Q2 / d^2
let's double Q1 and d
K 2Q1 Q2 / (2d)^2 = 2/4 (K Q1 Q2 / d^2) = 1/2 F or F/2

Coulomb's Law F = kq(1)q(2)/r^2

For the first case let the charge of one particles be m, the other n, and the distance s
For the second case the charge of one is m, the other 2n, and the distance 2s

plugging in:

Case 1: F1 = (k*m*n)/s^2
Case 2: F2 = (k*m*2n)/4s^2

Dividing F1 by F2 we get 1/2 (all the k, m, n and s terms cancel)

-> the force for the new case will be F/2