It's important to realize that magnetic field lines are abstract mathematical concepts, not physical realities. Their direction represents the direction of the magnetic field at a position in space, and their density represents the strength of that field. (The direction and strength of the magnetic field in turn yields information on magnetic forces, such as forces on moving charges.) Since the magnetic field is a vector that can point in only one direction at a given position in space, magnetic field lines cannot intersect. If there are two separate sources of magnetic fields, the net field at a point would be given by a vector sum of the separate field vectors.
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