Magnetism of particles
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A particle within an external uniform magnetic field tends to be oriented so as to minimize the total field (the potential energy of interaction) in the maximal space volume. The vortex is oriented by the torques, which arise in its external volume (outside the vortex ring filament). But the lightweight leptons (electrons), in contrast to the heavy hadrons, have a property of directing and closing a magnetic flux along an arbitrary path, which is specified by the external fields.
The paramagnetism and the ferromagnetism are caused by the magnifying reaction of the electrons to an external magnetic field. The diamagnetism is the minifying reaction of the protons and the neutrons, which make up the atomic nuclei. The material permeability is composed of the diamagnetic and paramagnetic components.
The Barnett effect is a magnetization of the rotating ferromagnetic objects as a result of the gyroscopic effect for the electrons. The inverse effect is the Einstein–de Haas effect.
The Faraday effect is a rotation of the polarization plane in a magnetic field, which is caused by the entanglement of the light beams by the aetheric vortices of the material particles. The vortices axes are directed mainly along the vector of the applied magnetic field, around which rotates the polarization plane. The rotation direction depends on the vortices direction, and therefore it is different for the paramagnetic and diamagnetic materials. This effect depends on the permeability and is proportional to the material density.
The definition of density ("Mass and inertia", 2) allows estimation of the average magnetic flux density inside the particles. Assuming that the particle is a sphere of radius \(R\), which is filled by an uniform magnetic field of density \(B\), this density is: \[B=\sqrt{\frac{3m}{4\pi\varepsilon_0R^3}}\tag{1}\] Substituting of the proton rest mass and \(R\) = 0,85·10^{–15} m gives a value \(B\) = 2,7·10^{14} T, which is 10^{14} times higher than a flux density of a strong permanent magnet.
The magnetic flux density in the particle bulk is very high, so a weak external magnetic field negligible affects the particle mass. Only a very small distance between the heavy particles alters their mass, for example, inside the atomic nucleus.
Two identical particles are always mutually attracted by their magnetic poles by one of the ways, which minimize the resulting field energy:
Pole attraction | Quantum spin | Bond | Examples |
---|---|---|---|
different | same | ortho- | Ortho-hydrogen |
same | different | para- | Pairs of the elementary particles, chemical bonds of electrons, and Cooper pairs. |
The quantum spin of the particles literally corresponds to the rotation direction of the same vortices with respect to each other.
The magnetic moment for any circle with radius \(r\) is \[IS=\frac{ev}{2\pi r}\pi r^2=\frac{evr}{2}\tag{2}\]
This circle consists of \(n\) circular wavelengths \[\lambda=\frac{2\pi r}{n}\tag{3}\]
Also according to ("Mass and momentum", 8), the wavelength of a particle or an aetheric beam is \[\lambda=\frac{h}{p}=\frac{h}{mv}\tag{4}\]
Substituting the equation (3) and (4) into (2) gives the equation, which is independent of radius and speed \[\mu=n\frac{eh}{4\pi m}\tag{5}\] where \(m\) is a whole particle mass.
The value (5) at \(n=1\) is called the magneton, and at \(n\neq 1\) it is called the anomalous magnetic dipole moment.
These circular waves are generally spatial, so their projections wavelength onto a circle can be shorter. This results in decrease of the \(n\) factor.
Particle | Magneton | \(n\) | Comment |
---|---|---|---|
electron | Bohr magneton | \(1,001\) | One period in a simple particle. |
neutron | nuclear | \(1,913\) | A cross between proton and electron. |
proton | \(2,793\) | Three periods is three quarks. |
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