Two point charges are separated by 6 cm. The attractive force between them is 20 N. Find the force between them when they are separated by 12 cm. (Why can you solve this problem without knowing the magnitudes of the charges?)

Solution 1P The attractive force between two point is separated by 6 cm is 20 N. Find the electrical force between the charges when they are separated by 12 cm. q q By coulomb’s law F = 12 2 r The ratio of the forces at the two distance F q122 6 = 6 F 12 q 122 12 2 = 122 6 144 = 36 = 4 The force at 6 cm is 4 times a large as at 12 cm. Thus the force at 12 cm is 20 N/4 = 5N. The charge attracting have equal magnitude, what is the magnitude of each charge From the coulomb’s law q q F = k 12 2 r q 2 = k 2 r 2 q = F× r k 20×3.6×10 3 = 9 9×10 2 -12 q = 8×10 12 q = 8 × 10 q = 2.83 ×10 C -6