Russell
"To exemplify our meaning let us remind you of the familiar belief that magnetism is a force, separate and apart from electricity, which has the power to pick up nails on a bar magnet and tons of iron on a giant magnet. Scientific terminology is redundant with references to such effects as magnetic lines of force, the earth's magnetic field, and electromagnetism, when every effect attributed to magnetism is solely electric. Furthermore, there is no such separate force as magnetism which performs the work of Creation. That which man thinks of as a magnetic force is spiritual Light of Mind and not a physical working force of Creation. Likewise, we hear constant references to negative electricity, negative charge, and negatively charged particles, which are as impossible in Nature as silent sound is impossible." [Atomic Suicide, page 103]
"If you place a lot of iron filings on paper, in the familiar way shown in all text books, and shake them over a magnet, those findings will form curved lines. These curved lines are called magnetic lines of force on that paper, and also in the so-called magnetic field of a planet. They are not magnetic lines of force. They are merely the curved planes of opposing pressures
[p. 187]
which electricity is causing in its efforts to compress." [Atomic Suicide, page 186-187]
"The universe does what it does. We humans try to explain what it does by postulating theories. Those of us who are better at this are called scientists. But these theories are just that, THEORIES. They are not the underlining principles that the universe uses. They are ONLY our humble attempts at discerning those underlining principles, which the universe is very good at keeping to itself. And no theory, even the ones that are so firmly established that we call them a "law", is ever the complete truth of those underlining principles.
Some scientists are so full of themselves that they allow themselves to think their theory is the end-all and be-all of science. These are what I think of as misinformed. No theory is ever complete or absolutely correct. This applies to those of Einstein. It applies to those of Hawkings. It applies to every theory that ever was proposed and to every one that EVER WILL. We simply do not have the minds necessary to get to the bottom of things. There is always some mystery that remains.
So, "magnetic lines of force", what are they? They are a very early attempt to understand and explain the magnetic force. I am not even sure they rise to the level of a theory. Someone with an interest in science, back in the 19th century observed that iron filings in a magnetic field (near a magnet) arranged themselves into groups and those groups looked like curved lines from one pole of a magnet to the other. This was an observation so it can be called an experiment. A small compass needle that was placed along those lines, another experiment, also oriented itself parallel to those lines. This tends to show that there are "lines" of force if you mean that you can follow one path from one pole to the other while traveling in the directions of the compass needle or those "lines" formed by the iron filings.
But part of the mechanism of the iron filings forming into lines is the size of those filings. Another experiment: if you use larger filings, you will get fewer "lines" that are wider. And if you use smaller filings, you will get more "lines" that are narrower. A further experiment would be to keep the magnet and the surface for the filings the same and removing and replacing the filings a number of times. Then you will get a different pattern of those "lines" every time you try that. The "lines" that are formed do not have any preferred position or arrangement.
These observations show additional things about a magnetic field. But they have their limits.
Current theory mostly refers to magnetism as a field. That simply means it has a value (note below) at every point in the universe. No points are left out, no matter how close they are to an adjacent point. Every point in the universe "feels" the magnetic force from that magnet that you hold in your hand. EVERY POINT! Even at cosmological distances, there are NO GAPS in this force. And this has been verified with many, many observations/experiments. So when your question is asked, the 19th century theory of "magnetic lines of force" breaks down and is no longer a good way of predicting what is actually happening in the universe. There are no individual lines: their number, if they can even be said to have a number, is infinite.
What that concept/theory of lines of magnetic force is mostly good for is predicting the direction of the magnetic field at a given point. An example of this is predicting the direction that the small compass needle will point. It is also good at getting the attention of grade school children in science class.
So the simple answer is, NO, there are no "individual" lines of magnetic force.
NOTE: Fields can have two types of values. Those with a single value at each point are called "scalar". Thus, the pressure in the ocean is a scalar value (PSI or other equivalent units) and the pressure field is a scalar field. It needs only one number at each point to fully describe it.. The other type of field is a "vector" field. A vector field needs a vector which has both magnitude and direction (at least two numbers) to fully describe it at each point. So the movements of the air in the atmosphere require at least two numbers fully describe them: the speed of the moving air (mph or feet per second or whatever) and the DIRECTION of that movement. The magnetic force is a vector field because both the magnitude and the direction of the force is needed for a full description." [Paul Alciatore]
See Also
Figure 7B.19 - Magnetic Lines of Force developed from Induction of Current Flow
lines of force