In a discussion about electron flow in an infinitely long conductor connected to two charged spheres, it is established that while the electric fields at points A and B may be zero, an electric potential difference is necessary for current to flow. The spheres, being conductors, allow electrons to move; electrons will flow from the positive sphere to neutralize its charge while excess electrons from the negative sphere will enter the conductor. However, the flow of electrons is directly proportional to the electric field strength, which diminishes as current flows, leading to a reduction in charge difference between the spheres. This results in a quick balancing of charges that ultimately stops the current. Therefore, while initial electron movement occurs, it is short-lived due to the rapid equalization of charge.