Georgina and Akinbo,
Thanks for the references, Georigina, I had perused the British Geo link and it goes to the Q vs. C question of:
Akinbo,
Good question if you are in for the long haul, because QM and Classical clash over what a field of any sort might be. I'll address the classical.
If we hypothesize a single material particle exhibiting a field which operates continuously from an electrical conductivity through a magnetic domain, both of which characteristic phenomenon each operate with a polarity in equal and opposite measure, and embedded in a unidirectional gravitational domain, all of those characteristic effects operating in accord with inverse square law; we might conclude as Faraday did that our hypothesis resolves from that full volume of field being a physical extension of the particle in a real material sense. That is the Unified Field famously sought by Einstein and many others.
Given that hypothesis, there is no physical boundary between the intensity at any chosen point in the field and a greater or lesser intensity at another chosen point. It changes as a smooth variation in a continuous physical function. So a line of force is very much like an isobar on the weather map, it is a continuous line of demarcation of a chosen measured value of intensity of whichever characteristic force effect is being plotted. But that can only be theoretical due to our limitations on experimental verification. We can not at the present, isolate and measure a single material particle.
In aggregate, the classical paradigm still lacks a rationale and conceptual rendering of how those distinct characteristic force effects can meld together and expand into a volume of an inertial frame envelope producing the ionosphere and magnetosphere and gravitational domain, while remaining discretely interactive with free particles and EMR. On the short haul, that is such a load that it was dropped in favor of the ad hoc, dice & slice methodology of Quantum Mechanics.
So in the whole earth catalog of aggregate effects, we might say that a magnetic line of force is an isobar of aggregate effect intensity as arbitrarily measured, and that spikes of intensity variation are anomalies of concentrations of particulate matter having a range of high magnetic moment inherent to a variety of isotopes.
I hope that doesn't muddy the waters too much, but its the best of my understanding in brief. jrc