Re: Magnetic N and S poles

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 14:14 -0500 12/15/01, John S. Denker wrote:
> I would be surprised and disappointed if _any_ textbook,
> introductory or otherwise, pre-1945 or otherwise, defined
> B in terms of the Lorentz force law.  By the same token
> I would be surprised and disappointed if _any_ textbook
> defined B in terms of N and S poles.
Well, I can't disagree with your pedagogy here, but, just to see what
the situation is, I pulled four texts off my shelf at random and here
are the results:

Halliday, Resnick and Krane, 4th Edition (1992), Page 737: After some
qualitative descriptions of magnetic phenomena they proceed:

We now define the magnetic field B in the following way, based on
these observations: The direction of B at point P is the same as one
of the directions of v (to be specified shortly) in which the force
is zero, and the magnitude of B is determined by the magnitude of
F(perpendicular) of the maximum force exerted when the test charge is
projected perpendicular to the direction of B; that is

B= F(perp)/qv.  (5)

At arbitrary angles, our observations are summarized by the formula

F=qvb sin (phi) (6)

where v is the smaller angle between v and B. Because F, v and B are
vectors, equation (6) can be written as a vector product:
F = qv x B              (7).

Once we get past the tortured and almost incomprehensible wording,
this seems to be a definition of B in terms of the Lorentz force.

Pasachoff & Wolfson, 2nd Edition (1995), Page 724: Essentially the
same thing, except that its worded much more clearly, but it
explicitly states that it is being defined in terms of a formula, and
that formula is the Lorentz force.

Serway & Beichner, 5th Edition (2000), Page 906: Almost identical to
Pasachoff & Wolfson. Again, explicitly using the Lorentz force to
define B.

Hecht, 1st Edition (1996), Page 790: I suspect you would be most
happy with this discussion of the magnetic field. He never defines it
as such, but gives several pages of descriptions of magnetic
phenomena which he interprets in terms of a so-called "magnetic
field." Only after lengthy discussions of Oersted, Ampere, Biot and
Savart, and their various laws, does he get down to the idea of
magnetic force and its relationship to the magnetic field via the
Lorentz force law. After a cursory survey of the chapter on
magnetism, I did not find a formal definition of the magnetic field
anywhere, but it might have been buried deeper than I had time to
look.

So, like it or not, it appears that about 3/4 of the texts out there
do in fact define B in terms of the Lorentz force. It may or may not
be the correct way to do it, but it seems to be popular.

Hugh
--

Hugh Haskell
<mailto://haskell@ncssm.edu>
<mailto://hhaskell@mindspring.com>

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