By applying Coulomb's law and taking into account that force is inversely proportional to the square of the distance, the force between the two particles after doubling the distance will be one fourth of the initial force.
Using Coulomb's law, we can predict the force between two particles when the distance is doubled. The initial force (Finitial) can be calculated using the formula F = kq1q2/r2, where k is Coulomb's constant (9.00 x 109 Nm2/C2), q1 is the first charge (-6.25 x 10-8 C), q2 is the second charge (2.91 x 10-9 C), and r is the separation distance (0.38 m). Once Finitial is found, to find the new force (Ffinal) after doubling the distance (r becomes 0.76 m), we apply Coulomb's law again with the new distance. Since the force is inversely proportional to the square of the distance, doubling the distance will decrease the force by a factor of 4 (22).
The initial force is:
Finitial = (9.00 x 109)(-6.25 x 10-8 C)(2.91 x 10-9 C) / (0.38 m)2
After doubling the distance:
Ffinal = Finitial / 4
In conclusion, after doubling the distance, the force will be one fourth of the initial calculated force.