Magnetic Field Lines: Why Are They There?

[JosephRombousky]

Magnetic field lines?

So I'v been taught throughout high school and now in college that a magnetic field has "lines of force". Also that they aren't just lines, but more like big shells around the magnet.

But not one of my professors or teachers could give me a reasonable answer as to why they are there. They don't seem to fit in with other forces that interact on macroscopic scales. Gravity doesn't have field lines, electrostatic forces don't have field lines, why should magnetism have field lines.

I read someplace about virtual particles interacting but that doesn't explain their increased spacing as you move away from the magnet. I expected it was a photon emission because it "can" sort of coerce to look like a interference patter of photons. But that it was bent killed that idea.

to be blunt : what is the deal with magnetic field lines?

 

[krab]

Where do you get that idea? Gravity has lines of force; so do electrostatic fields. For a given particle, they look boring because particles are monopoles. Magnetism is more exciting: the smallest unit is a dipole.

 

[JosephRombousky]

Ok if they do have lines, my question is still more broad,
what purpose do these lines serve, where do they come from?

How can we explain electromagnetic field lines besides just saying "its a physical property"(as i'v just repeatedly been told)

also how big can these field lines for gravity and electrostatic forces be?

Also how can any single magnetic particle be considered dipole? its just a matter of rephrence frame that gives it a dipole.

still spherical field lines around a charged particle pose me a problem..


(please be gentle, i ask because i want to know more, so excuse me if i sound silly)

 

[Tide]

Joseph,

There are no lines of force! It's a handy abstraction that helps us visualize fields which also happens to be remarkably useful. The notion originates from the fact that vector fields, such as an electric field due to a charged particle, have magnitude and direction at every point (another abstraction!) in space. If you follow the vector at a given point it leads you to a neighboring point at which the field may have another direction. Follow that vector and it leads you to another neighboring point and so on. The locus of points (trajectory) traced out in this manner constitutes what we call a line and, in the aggregate, they are "lines of force."

 

[pervect]

General relativity doesn't really treat gravity as a force, so it's not surprising that there isn't (as far as I know, anyway) any solid concept of "lines of force" in GR, except in the limit of weak fields where one can make fruitful anologies with electromagnetism.

However, there is a solid mathematical basis for "lines of force" in electromagnetism in the mathematics of two-forms. Unfortunately, this is a fairly advanced topic, though it can be made remarkably intuitive with a correct graphical approach.

It's really, really, really hard to do the topic justice in a forum like this though. MTW's "Gravitation" has a good treatment of the topic.

The electromagnetic force can be represented by the "Faraday tensor", a completely anti-symmetric second rank tensor. This tensor can be decomposed into a pair of "wedge products". Each wedge product has a graphical representation as an egg-crate like structure. These egg-crate like structures can be thought of as the lines of force - one for the electric field, and one for the magnetic. (Both fields are combined in the Faraday tensor).

 

[JosephRombousky]

I picked another question that is way over my head.
so perhaps someone can recoment a book or something i should order off of amazon so that i can learn about vector fields and faraday tensors?

But thank you guys, so far, a major help.

And maybe someone can give me an idea what particle this vector field is comprised of?

I know their are no "lines of force" that it is an abstraction, but back to simply putting iron fileings around a magnet, you'll end up seeing definite lines. So these lines are the vector field, what are they comprised of?

 

[Adrian Baker]

The lines you see with iron filings are simply the iron filings! They form into lines as each one becomes magnetised and they then form clumps which on a bigger scale gives us the lines you see.

The best way of visualising the magnetic and electric fields is to consider that in the space around a charge or a magnet, large numbers of 'virtual particles' continually pop in and out of existence (as allowed by the uncertainty principle).

These particles 'carry the force' between real objects. A simple picture is to visualise the magnet and the iron filing interchanging these particles between each other. This is what we call a field.

A good starting point in learning to understand some of these very odd concepts must be R Feynman's book QED. It is a fairly easy read without too much maths - that can follow on later!

 

[JosephRombousky]

OK i'v ordered QED on amazon.
i wasn't aware that the lines in the iron filings were simply the iron filings intereacting with each others induced magnetic fields, but that makes sence, I suppose i should think more about it

thank you very much. all of you have clarified this, and put me back on path.

But i don't understand why electrons spinning in parallel should ever have the capability of inducing virtual particles. since it would mean at every point if one electron has unpaired spinning, it itself would cause virtual particles to appear and everything should have an overal virtual particle mist...oh look i'v gone cross eyed.

Also more book suggestions are welcomed

another pain in my head.

If magnetism is caused by unpaired electron spins, would a free moving unbound electron have a spin? and would its spin cause it to emanate a magnetic field? Or could it just be considered paramagnetic? or spinless?
(my professors don't like my questions)

 

[pervect]

Any non-time varying force will have a static map between a point in space, and the associated force at that point in space.

This will also define a curve in space, which can then be considered to be a line of force.

The interesting thing about (for example) the electrostatic force is that while the direction of the lines determines the direction of the force, the density of the lines determines the magnitude of the force.

The density of the lines is determined by counting the number that cross a unit area oriented in a direction normal to the lines.

It is obvious that the total number of lines must be constant if the model is consistent. This gives a conserved quantity, which can be re-written as an intergal, the density of the lines per unit area * delta-area = total number of lines.

But the density of the lines per unit area is just the magnitude of the force, so we see that it is necessary that there be a conserved quantity, the intergal of the force normal to a unit area * delta-area.

This is just the intergal form of Gauss's law for electromagnetism.

 

[Adrian Baker]

But i don't understand why electrons spinning in parallel should ever have the capability of inducing virtual particles. since it would mean at every point if one electron has unpaired spinning, it itself would cause virtual particles to appear and everything should have an overal virtual particle mist...oh look i'v gone cross eyed.

Virtual particles appear in free space everywhere -you don't need a charged particle (or anything else!) to cause them.

It isn't easy to visualise what is going on in the quantum world - trying to form a mental picture is more often a hinderance than a help!

 

[EngineerCanuk]

I just joined this discussion on field lines after renewing an interest in Maxwell.

It sems to me that there are indeed no physical lines of force since the field (an idea atributed to Faraday who had almost no formal education) is everywhere at all points surrounding the magnetic source - not just along the lines we choose to draw.

A good book that I recently found is: A Students Guide to Maxwell's Equations which makes this point about field lines clear: the lines you count to indicate field strength are your own choice, so to compare field A to field B =2XA you could draw 5 lines per cm on A then 10 lines per cm for B. You could also draw 20 for A and 40 for B - its your choice but in fact the lines for each are infinite in number. The ral difference is the size and direction of the E vector at comparable points.