Question

why do not magnetic lines of force intersect with each other

Answer 1

$<font color="red"><h1>HELLO FRIEND</h1></font> <b><font color="green"><marquee>Here is your answer.</marquee></font></b><hr size=3 color="blue"> Magnetic lines do not intersect with each other because if they intersect then at the point of intersection there will be two different directions which is not possible so magnetic lines of force do not intersect which each other <hr size=3 color="green"><font color=#800080> <b>HOPE IT HELPS<BR>PLEASE MARK IT AS A BRAINLIEST ANSWER<BR>PLEASE FOLLOW ME</b><BR><BR></font><font color="red"><b>About me: </b><I>Shivam shaurya$

Answer 2

Magnetic field lined do not intersect each other because if there would be intersection between the magnetic fields then there would be two tangents which would represent two different distances.

But it is not possible practically to denote to two directions at the same time.

The magnetic fields would also come very close which is not possible.






There's a pellucid explanation:
A pure electromagnetic field cannot exist in the absence of a curvature of space. This curvature prevents the lines from crossing in a perfect field. The lines do converge at the extreme ends (the poles) of the magnet dipole moment. The results is that they vectorially sum to zero, meaning they cannot have a dimensionless property of charge. 
The search continues for magnetic monopoles (magnetic fields that imply a difference between ground states within that frame, e.g., a 'charge' potential) though none have been directly observed. There's some evidence to support the claim that they do exist, such as during CMEs that occur on the surface of the sun (sunspots) when magnetic field lines twist to the point where they break and release brehmsstrahling (brake radiation) as gamma radiation. 
What's interesting is if we @Hz/@ (make/break) a strong field at 0 cps, we still get a vector sum of 0 within the magnetic component of that field. We do get a torsion arising from that field (refer to above about the initial pellucid explanation of electromagnetic fields to that of curved space, add in Reinmann manifold theory and you have an even clearer picture of this) and that torsion is the result of the twisting of the local reference frame.
Imagine such a field, a coil into your monitor. Its field lines are large numbers of X marks that bulge in the center and converge at the top and bottom of your monitor.
Now imagine the same configuration, a coil into your monitor. If we pulse the coil (@Hz/@), we get an affine connection along with vectorial tension on the medium if so properly biased to the medium (the impedence of free space is 377 mhos/m) that's a torsional element. The torsion element is a tensor. The lines cannot cross in a single-mode non-isotropic solenoid. The connections balance at the extreme ends.