can two magnetic lines intersect each other when the magnets are perpendicular to each other? The magnetic lines would be produced by electricity.
[Physics] Can two magnetic field lines intersect each other when the magnets are perpendicular to each other
electromagnetismmagnetic fieldsVector Fields
Related Solutions
There is a difference between your two cases. When you are talking about a charge passing between magnets you are thinking of it as a uniform magnetic field. But it is not uniform, it gets stronger as you approach the magnets. if it were a uniform field the magnetic dipole you put in the middle would not feel a force along the line of the magnets, although it would still experience a torque.
To see where the force along the magnets comes from, imagine a single charge moving in a circle with velocity always perpendicular to the line of the magnets. If it were a uniform magnetic field the Lorentz force would act perpendicular to the line of the magnets producing an outward radial force. This is what you realized.
But really the field is getting weaker as you go away from the magnets, and since the magnetic field has no divergence that means the field lines must expand outward as you go away from the magnets. You see this on any diagram of the magnetic field of a dipole. So if you look at what the Lorentz force on the charge moving in a circle is now the the magnetic field has a (possibly small) component outwards you will see the charge picks up a force along the line of the magnets (in addition to the original force outward).
Here are from wikipedia drawings of the field lines of two magnets in two orientations, like-like, like-unlike .
North pole to north pole
North pole to south pole.
The lines distort but do not intersect.
These field lines are solutions of the formal Maxwell differential equations. Differential equations do not give discontinuous solutions, as would be the case if two lines crossed. Discontinuities in the solutions when smooth boundary conditions exist are not possible, as in the drawings. Discontinuities can exist as singularities, which can only exist at the source of the field. The field lines themselves follow smooth functions away from sources.
Mawell's equations have been continually validated by an enormous number of experiments and applications and thus we trust the descriptions of nature that the solutions give.
Best Answer
No, not in the sort of examples you're talking about anyway. Let me give you a real world example:
This is a topographical map. Do you see the brown lines? The represent locations of equal altitude. They don't exist, they're just lines on a map You won't see a brown line on the ground if you go there, nor do you expect to!
Now, do you see any of the lines crossing? Think about it for a second: if the lines crossed, that would mean that that spot on the ground has two different altitudes at the same time! That's not a thing. And what about the points between the lines, do they have no altitude? No, they're just not labelled.
Magnetic field lines are like these lines, they are not "real things", they are just a way of diagramming that makes it easier to understand. For topo maps we're making lines where the altitude is the same, for magnets, we're making lines where the magnetic field is the same.
Now I know what you're about to say... "but what about this:"
They look awfully real, don't they? But it's an illusion. Sprinkle the iron five times and you'll get five different patterns. They will be similar, but not the same. That's because they're not actually following some magic line in space, they're just getting magnetized and sticking to each other, it's a totally random process.