Magnetic Field Lines: Explaining Iron Filings Behaviour

[BJDJ2421]

The magnetic field surrounding a bar-magnet (for example) is continuous. The lines that are drawn to depict the strength and direction of the field don't actually exist. They are akin to drawing contours on an OS map, are they not? What therefore explains the behaviour of iron filings when they are scattered in the magnetic field of a bar magnet? Why do the arrange themselves along distinct 'lines', creating a pattern of peaks and troughs in the field? Does continuum or statistical mechanics offer an explanation the observed behaviour?

 

[Naty1]

try Wikipedia here:
http://en.wikipedia.org/wiki/Magnetic_field_lines#Physical_significance

 

[bjacoby]

The magnetic field surrounding a bar-magnet (for example) is continuous. The lines that are drawn to depict the strength and direction of the field don't actually exist. They are akin to drawing contours on an OS map, are they not? What therefore explains the behaviour of iron filings when they are scattered in the magnetic field of a bar magnet? Why do the arrange themselves along distinct 'lines', creating a pattern of peaks and troughs in the field? Does continuum or statistical mechanics offer an explanation the observed behaviour?

Yes, field lines are like a contour map. The explanation of the nifty behavior of iron filings is that when either the filings are longish pieces of metal or alternatively small chunks stick together to form longish pieces, you find that since the field magnetizes the iron making it a tiny magnet and they all are magnetized in the direction of the field The forces on the filing tend to rotate them to align with the field direction and then the end of one (say North) will also want to stick to the other end (south) of the filing right in front of it. Hence if you add some statistical randomness (shake the paper) one gets a pattern of stuck together filings that is highly suggestive of (but is not really) field "lines". It was probably these patterns that caused early electricians (as they were called then) to invent the whole lines of force theory which really causes more confusion than clarity.

 

[kcdodd]

Field lines are as 'real' as field vectors. Field lines are simply path integrals of field vectors, and field vectors are simply the tangents to the field lines. They both describe the same field.

However, they should be distinctly separated from equipotential, or contour, lines. Those imply a scalar value, not a field.

 

[sardar]

I would like to clarify that the magnetic field lines are not just a visual representation, but they actually represent the direction of the magnetic force at any given point in the field. The direction of the field lines show the direction in which a magnetic north pole would be pushed or pulled, and the closer the lines are together, the stronger the magnetic force is at that point.

The behavior of iron filings in a magnetic field can be explained by the concept of magnetic flux. When iron filings are scattered in the magnetic field, they align themselves along the magnetic field lines due to the attraction between the filings and the magnetic field. This creates a pattern of peaks and troughs in the field, as the filings are more concentrated along the stronger field lines.

Continuum mechanics and statistical mechanics can both offer explanations for this behavior. In continuum mechanics, the behavior of a continuous material, such as iron filings, is described by mathematical equations that take into account the properties of the material and the forces acting on it. In this case, the magnetic force is the dominant force acting on the filings, causing them to align along the magnetic field lines.

In statistical mechanics, the behavior of a large number of particles is described by statistical laws. In the case of iron filings, the individual particles have a random orientation, but when a large number of them are placed in a magnetic field, they tend to align themselves along the field lines due to the attractive force between the particles and the field.

In conclusion, the behavior of iron filings in a magnetic field can be explained by the concept of magnetic flux and can be further understood through the principles of continuum mechanics and statistical mechanics. These concepts help us to understand the underlying mechanisms behind the observed behavior and provide a deeper understanding of the magnetic field and its effects on materials.