# Magnetic Flux Quantization

I remember a few years back in my introductory AC/DC circuits class reading a little bit in the back of the book about magnetism. By this point, I was well aware that magnetic fields are commonly represented as lines of force denoting the direction of the field in a diagram. Iron filings would line up along these lines if used the right way.

What really puzzled me is what the book said regarding the unit of magnetic flux, the weber. It said that one weber was equal to 100,000 lines of force.

Is magnetic flux really quantized this way? Are lines of force not just a abstract representations of the field, but actual things that can be counted like electrons? Are all measures of magnetic flux integer multiples of 10 uWb?

If this is not true (and I suspect it is not), can anyone think of what they might have meant by this?

• What is quantized is the electro-magnetic field, but the static magnetic field is not quantized. What you saw as relationship between the weber and the lines of force doesn't seem to have to do with the quantum theory. Mar 7 '15 at 1:25
• A static magnetic field is a special case of an electromagnetic field and is in principle quantized the same way. Often, however, in specific applications, one treats a static magnetic background field classically. This is because quantizing the field would enhance the complexity of the problem enormously without any particular additional insight into the problem. But this does not mean that the field cannot be quantized. Sep 11 '15 at 9:22

What you are referring to is just the unit which is defined for the magnetic flux. It equals 100.000 lines of force (I did not check if this is true or makes sense at all; I am just assuming that the book is correct here. You can find an official definition of the unit "Weber" here: https://en.wikipedia.org/wiki/Weber_(unit)).

How a unit is defined - at the end - is just a convention. There is no physics behind it. You could also define a unit which equals 10.000 lines of force. Or one which equals 9345 lines of force. Also "lines of force" is a unit (depending on in what unit physicists measure force). As I said all of these units are just a conventions, an agreement among scientists in which unit they want to measure the magnetic flux. They have nothing to do with quantization at all. In principle, you can define any unit for a physical quantity as you like it. For example, we measure mass in units of kg. But, of course, mass is not quantized in kg. We can observe masses which have fractions of 1kg. We could equally use a different unit. It has no effect for the physics behind it.

But, on the other hand, the magnetic flux is indeed quantized: The flux through a superconducting loop comes in quanta with $$\Phi_0 = h/2e \approx 2.067833758(46) * 10^{−15} Wb$$

This is a very, very small fraction of 1 Weber and also a very small fraction of one line of force.

It means that any flux you measure will be a multiple of this small amount of flux. You will never observe a magnetic flux which contains a fraction of this amount. But you very well can observe magnetic fluxes which are fractions of 1 Web or which are fractions of 1 line of force (which is also a unit at the end and relies on the convention, in which unit the physicists measure force).

You could now, of course, define a unit which exactly equals this minimum quantum of flux.

Then any flux you will ever measure will have an integer value when you refer to it in this unit. In this case, the unit would have a physical meaning and would be a little bit more than just a convention (though it is still also a convention).

• Thank you for the thorough answer, and I apologize for the very belated Best Answer. Apr 20 '17 at 15:42

Since the magnetism itself is not quantized ( the magneton particle isn't prooved to exist experimentaly ), then niether can be its field quantized. I think they may have meant to explain a approximation, to have a clue how much a weber can be like. :/

• A magnetic field can in principle be quantized the same way as any electromagnetic field. The respective particle is the photon and not the magneton. Sep 11 '15 at 9:23