Coulomb measures a repulsive force of 20 x 10^-6 N between two charged spheres separated by 5.0 cm. He then brings the spheres to 3.0 cm apart without changing either charge. Using F_f = F_i (r_i / r_f)^2, what force does he now measure?

1. Coulomb's law gives F_f / F_i = (r_i / r_f)^2 when the two charges are unchanged. 2. Substitute r_i = 0.050 m and r_f = 0.030 m: (0.050 / 0.030)^2 = 2.78. 3. F_f = (20 x 10^-6 N)(2.78) = 5.6 x 10^-5 N. 4. Because the charges are unchanged and were the same sign to begin with, the new force is still repulsive. 5. Option B simply keeps the ratio-of-distances factor as 1, ignoring the inverse-square growth as the spheres move closer, which is the trap here. _Source: OpenStax Physics (CC BY 4.0), Ch 18 "Static Electricity", section 18.2 Coulomb's law_