Conducting current through a bar magnet can induce movement due to the Lorentz Force, which causes a slight horizontal deflection when the current is initiated or stopped. The discussion highlights the importance of the connections made between the battery and the magnet, as well as the role of conservation of momentum in the system. If the setup is fixed in space, the interaction between the magnetic fields of the wires and the magnet could theoretically produce a net force. However, the consensus suggests that if the current is directly attached to the magnet, there would be no net movement due to Newton's third law. Ultimately, the conversation emphasizes the complexities of electromagnetic interactions and the limitations of achieving continuous motion in this context.