What is the magnitude of the charges?

Question

Two-point charges, A and B, are separated by a distance of 23cm. The magnitude of the charge on A is twice that of the charge on B. If each charge exerts a force of magnitude 45N on the other, find the magnitudes of the charges.

Answer 1

Use Coulomb's law to show 45=9*10⁹QaQb/(.23)². Since Q_a=2Q_b the previous equation can be simplified to be 45=9*10⁹*2Q_a². Solve to find Q_a=.707*10^-4 C and Q_b=.354*10^-4 C