In a generator, the flow of electrons is induced by a voltage created when a conductor cuts through magnetic flux lines. The direction of the magnetic field does not need to align with the coil; rather, the maximum induced voltage occurs when the conductor moves at a right angle to the magnetic field. This interaction causes free electrons in the conductor to gather on one side, allowing them to flow when a load is applied. The relationship between the direction of movement, magnetic lines, and induced current is described by vector quantities that are perpendicular to each other. Understanding this phenomenon involves concepts from electromagnetism and the Lorentz force, which explains how charged particles interact with electromagnetic fields.