Comments on: Levitation and diamagnetism, or: LEAVE EARNSHAW ALONE!!!

By: Alan Haisley

Alan Haisley — Sat, 26 May 2012 14:34:26 +0000

This inverse square – inverse cube discussion is a diversion from the original discussion of Earnshaw’s law. Is it possible that any attraction or repulsion at a distance that follows any inverse power law at all will be unstable? Intuitively, whether it is inverse unity, square, cube, or even higher power, the static field model will be unstable.

By: skullsinthestars

skullsinthestars — Tue, 08 Mar 2011 15:45:45 +0000

When the Biot-Savart law is extended to the three dimensional case it becomes a third power law as it must.

You’re missing the point: Biot-Savart law *is* a three-dimensional law! The fundamental element of integration is still 1/r^2, regardless of whether one is integrating over a line, surface, or volume.

By: Evan

Evan — Tue, 08 Mar 2011 09:32:51 +0000

When the Biot-Savart law is extended to the three dimensional case it becomes a third power law as it must. As for what the standard model has to do with this discussion that depends on why you raised the question of monopoles. They aren’t relevant to Earnshaw’s Theorem but third power law most certainly is.

The simple point is that magnetism follows inverse third power law, not inverse square. While that doesn’t change Earnshaw’s it does affect your description of same.

By: skullsinthestars

skullsinthestars — Tue, 08 Mar 2011 02:58:57 +0000

(In any case, whether one calls magnetism and “inverse square” law or not is a relatively minor quibble for the purposes of the post, almost a semantic one. The important thing is that Earnshaw’s applies.)

By: skullsinthestars

skullsinthestars — Tue, 08 Mar 2011 02:35:57 +0000

The Biot-Savart Law applies to what is effectively a two dimensional case.

???? The Biot-Savart law is a fully three-dimensional law; I have no idea what you mean by it being “effectively” a two dimensional case.

The absence of monopoles isn’t just a convenience.

Nobody said it was. Discussions of the standard model don’t really add anything to the discussion of Earnshaw’s theorem.

Your assumption seems to be that the absence of monopoles somehow fundamentally changes the behavior Re: Earnshaw’s theorem. It doesn’t; Earnshaw’s theorem applies equally well to groups of electric dipoles or quadrupoles as it does to groups of point charges. Though there are certainly differences in the behaviors of electric and magnetic forces, they possess a very similar structure that is, as I understand it, all that is necessary for the development of Earnshaw’s theorem for magnets.

By: Evan

Evan — Tue, 08 Mar 2011 01:58:05 +0000

The Biot-Savart Law applies to what is effectively a two dimensional case. Because of that any effect will be described by second power law. An actual magnet is a volumetric entity and the force field produced obeys 3rd power law. That includes the magnetic field from a solenoid that is energized by a constant current. It IS the specific dipole field that constitutes the manifestation of magnetism as a component of the electromagnetic force. The absence of monopoles isn’t just a convenience. They are not permitted in the standard model. Any attempt to extend the standard model to include them requires either very early annihilation or absolute confinement similar to quark confinement.

By: skullsinthestars

skullsinthestars — Mon, 07 Mar 2011 16:22:19 +0000

You may be thinking about the specific dipole field, which does obey an r^-3 law. The Biot-Savart law, however, which describes the magnetic field of an infinitesimal current element and is in essence the analogy to Coulomb's law for electrostatics, is an r^-2 dependence. In essence, magnetism is also inherently an inverse square law force -- the absence of magnetic monopoles then makes the dominant contribution to this force an inverse cube one.

By: Evan

Evan — Mon, 07 Mar 2011 12:06:25 +0000

There is a major fly in the ointment in respect of your explanation.

You wrote: “Such a law is followed by gravity, electricity and magnetism” (inverse square). This is not true of magnetism. Magnetism follows 3rd power law and dimishes with the inverse third power of distance.

By: Art Unwin

Art Unwin — Thu, 24 Feb 2011 04:43:44 +0000

Please note comment above regarding Levitation and diamagnetism
as I failed to notify you when I posted it
Regards

By: Art Unwin

Art Unwin — Fri, 04 Feb 2011 06:03:53 +0000

Sir
Another way of convincing others to your line of thought is via the explanation of radiation and it connection to the two vectors of the Standard Model as espoused by Einstein.
Radiators are made of diamagnetic materials which contain the two vectors of gravity
and rotation of the Earth when excited by a time varying field. This is made quite clear
when a time varying field is added to a Gaussian static field where the mathematical
result is the equal and the same of Maxwell’s equation for radiation.
The two vectors of the Standard Model provides not only the spin as required for maintainance of straight line projection of a resting particle on a diamagnetic surface
of a radiator together with the counter gravity vector which is required for straight line trajectory as seen with radiation where each particle or unbound electron is accelerated carrying a digital sample of communication.
When a time varying field is applied to a radiator the skin effect for resistance is removed along with the external magnetic field such that the current exits from the radiating member up to the under surface provided by residing particles where the two vectors supplied are equated as the acceleration forces of charge.
On the other hand, the above finally removes the idea of waves with respect to particles as far as radiation goes together with arguements with respect to the Eather where surface waves are now explained via the change in medium between unbounded electrons and the surface that they reside upon.,

The above is easily corroberated by winding a pancake radiator which is the equivalent to a Gaussian field in equilibrium which, with the maximum density of wire surface , correlates with maximum residing static particles for the creation of loss less radiation.
With your love of the use of vectors as explanation points radiation provides a platform for not only the explanation of radiation but also of levitation, the Std model,
the removal of skin effect resistance in a radiator, and also an explanation of diamagnetics with respect to the surface skin of static particles on water when subject to a magnetic field
Regards
Art