Hello,
They form continuous curves because field lines begin from north and end in south side. hence they form closed curves. :-)
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It's not correct that magnetic field lines are always closed loops. They can, for instance, extend to infinity in both directions. Or they can loop endlessly around some small volume without touching themselves- after all they are just mathematical objects with zero thickness. But what they can't do, & I assume this was your point, is end. More generally, you can look at some region in space- any shape you like & anywhere you like- and the total of the magnetic field entering & leaving it will always cancel perfectly to zero. Mathematically, this is called zero divergence.
Electric fields, on the other hand, can have plenty of divergence- anywhere you have electric charge, there are lines of force streaming out of it (or into it, depending on the sign of the charge) . The divergence is exactly proportional to the amount of charge. But not all of the electric field comes from charge- some comes from changing magnetic fields, and that part (if you are careful to split up the field in a very specific way) does have zero divergence.
So what would create magnetic fields with divergence? Obviously, magnetic charge! Now we just have to go find some. All the magnetic fields we see come from movement or spin of electric charges. Magnetic ones, called magnetic monopoles, could fit very nicely into our theories, but so far as we know, they just don't happen to exist. There are some experiments searching for them, and some models that say they should exist- a few in the universe- but so far, we more or less assume that electric fields have the monopoly (ha-ha) on divergence & charge.
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