Each loop in the solenoid will have its own magnetic field wrapped around it. In that case it won't resemble the magnetic lines formed by a bar magnet…; but we see that it is the same. Why is that?
[Physics] Why in a solenoid, do the magnetic field lines resemble that of a bar magnet
electromagnetisminductancemagnetic fields
Related Solutions
The "lines" you see when viewing iron filings around a magnet have more to do with the fact that they are tiny slivers of iron, and less to do with magnetic field lines as one normally talks about them.
Also, over the length scale of one of these slivers, the magnetic field is largely constant, and a ferromagnet (or magnetic dipole) placed in a constant magnetic field will not accelerate (it will, however, align itself with the field). Once two slivers line themselves up head to tail, the field they create around them makes it more favorable for other slivers to join the chain rather than to lie haphazard, because the filings distort the field around them. So it is simply energetically preferred for these slivers to line up head to tail and form longer chains, but if you look closely, the chains break and merge.
Magnetic field lines are just a way of visualizing magnetic fields, in the same way that electric field lines are used to visualize electric fields (lines of force). There are no "gaps" between true magnetic field lines -- they occupy all space. We just draw them that way to convey a sense of their intensity.
I also don't quite agree with the statement that friction prevents them from clustering on the magnet. It's a bit more complicated than that, and, indeed, you can watch the same behaviour in air by suspending a magnet above the filings and allowing them to lift up. Once the filings start attaching themselves to the magnet, a magnetic circuit is created which changes how the field looks.
It comes down to what user3814483 said in his comment: it's just a linear superposition of fields due to the coil and the "magnetized" (i.e. aligned) ferromagnetic dipoles. However, the aligned dipoles exert fields on each other in addition to the pre-existing coil field. These 'mutual fields' are so strong in comparison that they cause alignment different than what the coil field would dictate by itself. However, I do not have a method to calculate what exactly the resulting vector field should be in this sort of situation.
To go back to first principles a bit, the only thing that actually 'exists' when it comes to magnetism is a magnetic (vector) field, which is quantified by the 'magnetic flux density' $B$ at each point. (Despite 'magnetic flux' $\Phi$ sounding like a more fundamental quantity, it is merely a mathematical construct to represent the surface integral of $B$.)
Cnly moving point charges have been observed to generate a magnetic field, and the 'source strength' of one (or many) of the these moving charges is defined as the magnetic dipole moment $m$, which relates torque to magnetic flux density: $\tau = m \times B$. The magnetic dipole moment magnitude can be conveniently calculated as the product of planar current enclosing an area: $|m| = IA_{enc}$. See https://en.wikipedia.org/wiki/Magnetic_moment for more info.
As you may be aware, atoms have electrons which 'encircle' them, and therefore create their own magnetic dipoles no different qualitatively than the one generated by a current-carrying loop. In ferromagnetic materials, these magnet dipoles can more easily get aligned in the same direction, thus multiplying the pre-existing field. This is no different than having two electromagnet coils on well-lubricated gimbals: if you were to flow current through each coil, magnetic Lorentz forces would cause alignment and result in an overall amplified field.
Therefore, the 'field distortion' in your core-wound example is due to the strength of the ferromagnetic dipoles overpowering/burying the field generated by the coil. And although the term 'channel' or 'concentrate' is often used to explain the high-level phenomena of a ferromagnetic material in an ambient field, that is not actually what is going on. The original field still exists, it's just that the alignable dipoles of the ferromagnetic material have settled to overpower the original field and make it look that way. Again, I don't have a way to describe why the resultant field comes out the way it does -- that's more in the domain of FEA.
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Best Answer
By applying Fleming's Right Hand in each turn, we get magnetic field lines that look like this :-
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But Magnetic field lines never intersect. They interact with the fieds of the surrounding turns of solenoid to form a combined magnetic field which looks like this:-
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From www.nde-ed.org :-
If the loops or turns are extremely close to each other, magnetic field lines between neighbouring turns effectively cancel, resulting in straight magnetic fields inside the solenoid, similar magnetic fields inside a bar magnet :-
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The magnetic field lines around (a) a bar magnet and (b) a current carrying solenoid :-
EDIT
As in the case of bar-magnets, the magnetic field is stronger inside the solenoid than outside it. Magnetic field lines are closely packed inside the solenoid, and magnetic field is concentrated into a nearly uniform magnetic field inside the solenoid. The magnetic fields outside are weak and spread out.
ATTRIBUTION
The first three diagrams are snipped from a video available on YouTube: Concepts in physics - Electromagnetism