Magnetic field lines do not cross each other because, at the point of intersection, the compass needle would have to point towards two directions simultaneously, which is not possible.
Why do magnetic field lines not cross each other, and what would happen if they did?
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Magnetic field lines do not cross each other due to the fundamental principle that they represent the path a north magnetic pole would take in response to the magnetic field. If lines were to cross, it would imply conflicting directions for the magnetic field at that point, making it impossible to determine the magnetic pole’s path accurately. This non-crossing nature ensures a unique and consistent direction at any given point, crucial for understanding magnetic phenomena. If magnetic field lines were allowed to cross, it would violate this fundamental principle, leading to ambiguities and inconsistencies in describing and predicting magnetic behavior. The non-crossing property is vital for principles like superposition and the conservation of magnetic flux, maintaining the integrity of magnetic field representations and facilitating accurate analyses of complex magnetic systems.