Sunday, July 12, 2015

\(S\) Pole Or Else

From the post "Not Exponential, But Hyperbolic And Positive Gravity!" dates 21 Nov 2014, we derived an expression for the force density \(F_{\rho}\) around a particle due to its energy density \(\psi\).  The general shape of the curve for \(F_{\rho}\) is,


but this is force density around the particle not the force as expected in a field around the particle.

As diamagnetism opposes the applied magnetic field, the general curve of \(-F_{\rho}\) applies instead,


If diamagnetism is due to temperature particles, then the "diamagnetic force density" around the particle will also have the same general shape.

Temperature increases as \(\psi\) for a temperature particle increases.  If \(\psi\) increases by the increase of \(x_a\) along \(x\), from the post "Not Quite The Same Newtonian Field" dated 23 Nov 2014.  An increase in \(T\) corresponds to an increase in \(x\) (assumed linear).  Then the force density at a fixed point around the particle also changes by moving along \(x\) as \(T\) changes.  The plot of force density at a fixed point changing with temperature \(T\), is then the plot of \(-F_{\rho}\) with the \(x\) axis replaced by \(T\), temperature.

When diamagnetism dominates in ferromagnetism (assuming that paramagnetism + diamganetism = ferromagnetism). then a plot of "ferromagnetic force density" changing with temperature \(T\), will be the general curve of \(-F_{\rho}\) added to the paramagnetism vs temperature plot .

Similarly, a plot of anti-ferromagnetism (assuming that paramagnetism - diamganetism = anit-ferromagnetism) will be the general curve of \(F_{\rho}\) added to the paramagnetism vs temperature plot.

Magnetic susceptibility, \(\chi\) is a dimensionless constant.  But \(\chi\) is often derived from,

\(\chi={\chi_{mass}}.{\rho}\)

where \(\rho\) is the mass density of the material and \(\chi_{mass}\) is obtained by dividing a measurement with the mass of the sample material, as such \(\chi\) is a density value, per unit volume of the material.  And we obtain the theoretical curves when diamagnetism dominates,


In this model, ferrimagnetism is ferromagnetism but the diamagnetism that comes to dominate the material magnetic behavior below Curie point, can cancels paramagnetism totally and gives zero magnetization, at the magnetization compensation point.  It is also possible to change the angular momenta of electrons such that paramagnetism increases to cancel diamagnetism.  This occurs at the angular momentum compensation point of the ferrimagnetic material.

It is tempting to equate paramagnetism with temperature particles, but increasing temperature would then increases paramagnetism.  When paramagnetism is equated to angular momenta of electrons, increasing temperature increases electron spin (not orbital rotation) that decreases its electric nature as energy oscillating in the orthogonal time dimension \(t_T\) of the wave/particle, manifest itself (ie. magnetic, \(B\)).   In effect the orbiting electron is more of a orbiting temperature particle, the magnetic momentum due to its rotation is reduced.  This is consistent with decreasing paramagnetism with increasing temperature.  The orbiting electrons behave like small electromagnets that is always on.  They will align themselves in the direction of an applied magnetic field and will always be attracted to the applied magnetic field.

Diamagnetism in this model is at the particle level.  Like particles will repel each other.  At above zero temperature, positive temperature particles are repelled by the \(N\) pole of a magnet.  At temperature below zero, negative temperature particles are repelled by the \(S\) pole of a magnet.  This assumes that at zero temperature there is no temperature particles.

Is diamagnetic levitation at low temperature achieved with the \(S\) pole of a magnet?  A \(N\) pole should  not levitate a diamagnetic material at low temperature.

Otherwise this model fails.