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Why never clockwise? How does it 'know' to go anticlockwise?

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The magnetic field is not a "vector", instead it is a bi-vector (skew-symmetrical tensor). In other words, it has a plane of action not direction. Here is a quote from Hermann Weyl "It may be justifiable on the grounds of economy of expression to replace skewsymmetrical tensors by vectors in ordinary vector analysis, but in some ways it hides the essential feature; it gives rise to the well-known “swimming rules” in electrodynamics, which in no wise signify that there is a unique direction of twist in the space in which electrodynamic events occur; they become necessary only because the magnetic intensity of field is regarded as a vector, whereas it is, in reality, a skewsymmetric tensor (like the so-called vectorial product of two vectors). If we had been given one more space-dimension, this could never have occurred"

and " ... when a magnetic field acts on a current element, whatever the inclination or orientation of the element at a given point, the force invariably acts in a locally fixed plane—Ampere’s directive plane—which is perpendicular to the conventional direction of the magnetic field", see for details John Roche "Axial vectors, skew-symmetric tensors and the nature of the magnetic field" Eur. J. Phys. 22 (2001) 193–203.

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    $\begingroup$ This is all true as far as it goes, but I'm not sure that it is helpful in the context of this question. Elementary treatments all present the magnetic field as having a direction and then give a (arbitrary sounding) rule for how to determine that direction. $\endgroup$ Jan 23 '15 at 17:44
  • $\begingroup$ You have just made my point: "arbitrary sounding" rule. It is just as elementary to think in terms of a plane of action as it is of a vector. Maybe it is time after 150 years of wrong teaching to have a new way that is correct, not confusing and not arbitrary. My comment is then helpful to the novice to learn that. $\endgroup$
    – hyportnex
    Jan 23 '15 at 17:58
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    $\begingroup$ These treatments are generally presented to students who don't have the mathematical preparation to take the phrase "skew-symmetric tensor" and do anything with it. They generally don't know what a tensor is, much less have the grounding to recognize the implication of skew-symmetry. $\endgroup$ Jan 23 '15 at 18:52
  • $\begingroup$ It seems to me that defining the magnetic field in terms of a plane of action does not relieve the arbitrariness, since the plane still needs to have a forward-oriented side and a reverse-oriented side. (If a current lies in the plane of action, the direction of the force on the current is still ambiguous.) $\endgroup$
    – pwf
    Jun 7 '18 at 21:01
  • $\begingroup$ @pwf you are right about that but note that now arbitrariness is only in which current direction we define as positive or negative, after all they are affected in opposite direction. Once we settle on that there is no arbitrariness and no need for "swimming rules". $\endgroup$
    – hyportnex
    Jun 7 '18 at 21:07
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The direction of the magnetic field is defined in terms of its effect on a current (or moving charge). Specifically, the magnetic field points in a direction such that the force on a current will be in the $\vec{I}\times\vec{B}$ direction. (That's just a convention; there's no fundamental reason you must define the magnetic field direction that way.)

Meanwhile, parallel currents are observed to attract each other, so we know one current is producing a magnetic field and the other is experiencing it. If you work out which direction the magnetic field around the first current must point in order for $\vec{I}_2\times\vec{B}$ to point towards the first current, it's in the right-hand sense (or anticlockwise around the first current if the current is pointing towards you).

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It is simply because of the convention we use for Field Lines. A different configuration would make it have a different direction.

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Because somebody decided to have clocks running clockwise, and all clockmakers since then followed suite.

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    $\begingroup$ Clock dials were designed to mimic the chirality of sundials in Northern Hemisphere. If the clock had been invented south of the Equator, it would be the other direction. $\endgroup$
    – Fred Kline
    Jan 23 '15 at 14:30
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    $\begingroup$ Sun dials placed on walls run counterclockwise, don't they? But nevertheless: there is something behind sun , earth rotation, direction of current and magnetic field. Faraday imagined a current in the earth running the same direction as the apparent path of sun producing the earths magnetic field. $\endgroup$
    – Georg
    Jan 23 '15 at 15:03
  • $\begingroup$ The clockwise is sunwise in the northern hemisphere of earth in this version of the universe. $\endgroup$
    – dan
    Jun 29 '15 at 19:12

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