How many times n should the value of one of the charges be changed when the distance between

How many times n should the value of one of the charges be changed when the distance between the charges decreases by 2 times, so that the interaction force remains the same?

Let us write the expression for the interaction force for the initial position
F1 = k * (q * q1 / r1²).

Interaction after changing distance
F2 = k * (q * q2 / r2²).

Let us write the equation with the equality of the interaction forces
F1 = F2;
k * (q * q1 / r1²) = k * (q * q2 / r2²);
r1 = 2 * r2;
k * (q * q1 / (2 * r2) ²) = k * (q * q2 / r2²);
q1 / (2 * r2) ² = q2 / r2².

Let’s find the ratio of the magnitudes of the charges
q1 / q2 = (2 * r2) ² / r2² = 2² / 1² = 4.

Answer: the value of one of the charges must be changed 4 times.