The case of two charges that magnetically interact can be discussed in a much simpler manner. We are all familiar with the concept of potential energy and know that kinetic energy is not separately conserved : only the sum of kinetic and potential energy is. In special relativity energy is the time component of four momentum. For the same reason kinetic energy is linked to kinetic momentum , potential energy is connected to potential momentum. The electromagnetic vector potential should thus be seen as producing potential momentum. While kinetic momentum, $m\bf v$, is not conserved, the sum of kinetic and potential momentum, $m{\bf v} + q\bf A$, is conserved in the case of two magnetically interacting charges.
