Question

Why do two magnet field lines never crossed each other

Answer 1

If the two magneticfield linesare intersecting and you place the compass at that point you know that the compass cannot point at two directions at once . So there will be only one direction shown by the compass and hence they do not intersect each other.

Answer 2

two magnetic fields never cross each other because :

at the point of intersection a tangent can be drawn and the needles would be found pointing in two different directions which is not possible.

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