Two point charges, A and B, are separated by a distance of 19.0 cm . The magnitude of the charge on A is twice that of the charge on B. If each charge exerts a force of magnitude 45.0 N on the other, find the magnitudes of the charges.

QA = 19μC

QB = 9.5 μC

Explanation:

The force that each charge exerts on the other must obey Coulomb's Law, as follows:

       

We know that the value of the magnitude of FAB  is 45.0 N, the distance between QA and  QB is 0.19 m, and that QA = 2*QB.Replacing in (1), we can solve for QB, as follows:

     

Since QA = 2*QB⇒ QA = 2* 9.5μC = 19.0 μC⇒ QB = 9.5μC