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I recently went to Antarctica where we made many shore excursions with Zodiacs. On one of them we visited the Ukrainian Vernadsky Research base on Galindez Island where they conduct geophysics research.

I was discussing this with one of the scientists there who was trying to describe his work. His English was not great and he was probably talking down to me as a non-specialist, but he very clearly indicated that he was studying the way charged particles from the sun cause perturbations along geomagnetic lines of force over great distances. And on a piece of paper he drew one such line that he was studying which he showed as descending to earth in New England (where I live) and said they were doing this research with Boston College.

My Question: I always thought that the idea of a "line" of magnetic force was conceptual convenience, an artifice we used to be able to talk about magnetism but that there are no actual, physical discreet "lines". And that the visual lines that form with, say, iron filings, are just due to the magnetized filings attracting others around them and so are just clumping artifacts of the filings themselves.

But this scientist seemed to be specifying a very specific line including a specific location near Boston where it descends to earth and drew it that way on a piece of paper and said they had been studying this particular line for years during different cycles of solar activity. What could he have been referring to?

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Geophysicists are not referring to specific lines of force, but instead study major long-term features or "lobes" of the earth's geomagnetic field. Apart from the main dipole, the field has more local features associated with more rapid change. These are hypothesized to originate somewhere in the core-mantle boundary and share some interesting relationships with the main dipole's excursions and flips.

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As pointed out already, the magnetic field is continuous and not made of discrete lines of force in a literal sense, but field lines are an effective way to represent the magnetic field vector, akin to stream lines for fluid flow.

What your scientist was likely talking about is a connection between New England and Antarctica as geomagnetic conjugate points at opposite ends of a magnetic field line where it meets Earth's surface. Indeed, for recent years, a field line from Galindez Island would land in New England.

A magnetic field line exiting at Galindez Island, as given by the IGRF-12 at 20170315T173300, landing somewhere in New England.

Various phenomena lead to charged particles and radio waves (like lightning whistlers) being guided along magnetic field lines. Studying conjugate points lets you observe aspects of the same phenomenon in two places

WJB
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There are no actual discrete physical lines, (except connected with superconductivity), there is a continous magnetic field. My guess he was simply placing a strong emphasis on a particular direction of the field in which the particles travelled. My knowledge of geophysics is very limited, perhaps there is some aspect of the terrain in the "landing zone" of the particles that is particularly important, but there are no field lines in reality.

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I always thought that the idea of a "line" of magnetic force was conceptual convenience, an artifice we used to be able to talk about magnetism but that there are no actual, physical discreet "lines".

You are correct, there are no magnetic field lines as actual physical quantities. Similar to vector field maps (i.e., plots with arrows indicating direction and magnitude by pointing and size, respectively), field lines are a useful visualization tool. Field lines are basically the "connect the dots" version of a vector field map (perhaps, overly simplified but basically true).

And that the visual lines that form with, say, iron filings, are just due to the magnetized filings attracting others around them and so are just clumping artifacts of the filings themselves.

Iron filings "line up" with the magnetic field to minimize the inner product $\boldsymbol{\mu} \cdot \mathbf{B}$, which is just the magnetic potential energy of a magnetic moment, $\boldsymbol{\mu}$, in an external magnetic field, $\mathbf{B}$. This happens to correspond to an approximate field line representation because the magnetic domains comprising the magnetic moment are aligned parallel to the length of the little cylindrical pieces composing the filings.