# Why are magnetic field lines imaginary?

There are many sources online which say that magnetic field lines are imaginary such as Toppr, Vedantu and CBSE Academic.

I do know that magnetic fields are real and do exist. But when can we see magnetic field lines using Magnetic Field Viewing Film? Why are they called imaginary?

• Who said that they're "imaginary"? Jul 31, 2022 at 8:53
• Your link is blocked in my region, or so it seems. However, my question was more about what meaning you assigned to "imaginary". Those lines are a mathematical representation of a vector field, so they have nothing to do with imagination. Jul 31, 2022 at 12:27
• I am definitely no expert here, but you know how ferrofluid makes spikes? I believe the reason for iron filings appearing to make lines are formed the same way ... Each spike (or filing) becomes itself a magnet. The tips of the spikes are the same pole - so the spikes repel each other. There's a "balance point" where the repulsion and attraction are even. Jul 31, 2022 at 22:33
• By "imaginary", they mean to say that they are abstract, as opposed to physical. I have seen this kind of language in children's textbooks in India many times. For example, I have also seen the claim that the axis of the earth is an imaginary line Aug 1, 2022 at 14:26
• I suppose the obvious counter-question to anyone making this assertion would be: what would it mean for a line to be real? Aug 2, 2022 at 16:53

Most of us will have experimented with placing iron filings around a magnet to get this sort of thing:

This particular example is taken from Why iron filings sprinkled near a bar magnet aggregate into separated chunks? The iron filings line up in the direction of the magnetic field and this nicely shows us what the field looks like.

Your magnetic field viewing film works in a similar way. It contains flakes of nickel that line up with the field in the same way as the iron filings, and this produces a pattern that shows us what the field looks like.

The magnetic field is certainly real, and it has a direction at every point in space, but the field lines are just lines that trace out the direction of the field. They are no more real than contour lines on a map are real.

• It might be worth explicitly pointing out that the filings form discrete lines because they actually affect the magnetic field in their vicinity. A larger scale version would be paper clips in a magnetic field forming a chain. The paper clips and iron filings aren't being attracted to a pre-existing feature of the magnetic field, they're reshaping it as they themselves become additional magnets and cling to each other in chains. Aug 1, 2022 at 14:38
• Contour lines on a map are real, but they're not usually drawn out in the landscape represented by the map :) Aug 2, 2022 at 11:32
• Is it really true : " and it has a direction at every point in space "?
– user326901
Aug 3, 2022 at 8:45
• @An_Elephant I suppose if the field is zero then it has no direction. But apart from this special case yes it's true that the magnetic field has a direction everywhere in space. It is a vector field so by definition it always has a direction because it's a vector. Aug 3, 2022 at 9:07

This dates back to Faraday. He was a brilliant experimenter, and he discovered a whole lot about electromagnetic stuff. But he didn't do math, and his explanations for what he found were not in mathematical form.

Some other physicists of the time didn't like him, and they didn't like his explanations, and they tried to say he was wrong. Except his explanations were easy to understand, and they did seem to fit the reality.

When you spread iron filings they tend to line up in long lines, for complicated reasons. Each filing turns into a little magnet which affects the field, so instead of just sitting in random positions and turning with the field, they move into line. You get little stringy strong fields and weaker fields in between. When the filings aren't there, the magnetic field is smooth and continual, and it doesn't have individual strong lines in it.

So they wanted to say he was wrong. People who imagine individual lines instead of imagining a smooth field are doing it wrong.

That argument kind of got fossilized. Educators still point out that the lines of force aren't real, because they know that's what they're supposed to say even though nobody really cares about discrediting Faraday any more.

Incidentally, if you draw a picture of a magnetic field with vectors, the vectors are also imaginary. There are no actual arrows, there's only a continuous bunch of points and at each of them the field has a strength and a direction.

Do you care?

• I don't think it was an attempt to say that Faraday was wrong. I've often read in textbooks the definitions like "an imaginary line located at 0 degrees latitude" (and even in Wikipedia) and other such "imaginary lines", and what is common to these definitions is that they seem to try to say "don't go searching for this line, it's imaginary, pure geometry, not a string of material". Jul 31, 2022 at 12:55
• I read a history that said they were trying to say Faraday was wrong in general, so this does fit into that. But your more charitable interpretation also makes sense. Jul 31, 2022 at 13:18
• Who are the "they"? [I ask only out of interest.] Jul 31, 2022 at 15:55
• "You get little stringy strong fields and weaker fields in between." - therein lies the flaw with this argument; this phenomenon is emphatically not what we mean by field lines in the primary sense of the term (even though we say that it helps us visualize field lines in some looser sense) Aug 1, 2022 at 3:04
• Another thought bubble is that the opposite happens if you look at say a field of wheat. If you observe it from a high distance, especially once it is mature, you might think of the wheat being almost continuous and not being made up of individual ears or heads of wheat. Even more so, if you looked at it closely when it was still young, you would see (at least if is planted using mechanical seeder) the wheat was actually planted discrete rows, and so might see it as a field of lines. Only once it grows do the plant heads tend to overlap and no longer can you easily see how they were planted. Aug 1, 2022 at 4:18

Any field is defined as the normalized force acting in a place on an object. Normalized means: if the force is proportional to some kind of "size" of this object, then the field strength is the force acting on that object of size one.

So the question: is there a "field" when there is no object can not be finally answered. No object can be in a place if not moved to there and no object can be changed in size without removing a part of it, as moving an object in a field means transfer of energy, the field may be produced just by bringing objects to the place.

But the lines created by the filings obviously represent reality, so you can call them field lines as they are strongly depending on the existence of a magnet.

But you have to realize: iron concentrates the magnetic field by about 10,000, so every line of iron gives a path to the magnetic flux leaving the direct neighborhood free of the field. Therefore the actual lining of the filings is a question of probability and the picture will be different whenever you repeatedly drop filings.

The lines that result from magnetisable filings are real. The representation of magnetic lines presents excellently how the magnetic field runs. What is still missing is the description of the discontinuum of the field, i.e. its description by means of particles. Physics still lacks an understanding of this.

It should be possible to describe the electric field, the magnetic field and the electro-magnetic radiation on the basis of particles. As long as this quantisation (discretisation) is not carried out, the question of the reality of field lines remains undecided. In a model of discrete particles, with which an electric field, a magnetic field and also EM radiation can then be described, field lines must then be a component of the description.

• Why should magnetism be carried by particles? Classically, magnetism depends entirely on the velocities of the charges. If the source charge is not moving, there is no electric field. If the target charge is not moving, it is not affected by the field. We detect magnetism only when both charges are moving. It depends entirely on the chosen frame. That tells me that magnetism is just a fudge factor. Our representation of electric force is flawed in a way that doesn't properly account for velocity, and the magnetic fudge factor is required in some frames. Why should it be quantized? Aug 1, 2022 at 8:25
• Electromagnetism is mediated by photons, so yes it's quantized. Aug 1, 2022 at 19:10
• Electromagnetic force is created only by charges, continuously and constantly, and there are only a finite number of charges in the universe so of course it's quantized. But magnetism is not quantized. If you are in the frame of the a charge that's the source, or a charge that's the target, you will not observe any magnetism. The force is all electrical. If you are in some other frame, the force will be partly electrical and partly magnetic. Magnetism is a fudge factor required because our measurement of electromagnetic force in frames doesn't add up without it. Aug 2, 2022 at 1:37
• But for radiation, the electric force and magnetic force are defined to be in exact proportion to each other. So I guess in that case the magnetic part of the radiation must be quantized exactly like the rest of it is. Aug 2, 2022 at 1:44