Difference between revisions of "Magnetism"
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The speed of an aetheric beam is the transfer speed of its magnetic field, therefore both the speed and magnetic fields have a lot in common. In particular, both fields of a rotating beam have a common axis of rotation, so the [[wikipedia:Curl (mathematics)|curls]] of these fields are [[wikipedia:Collinearity|collinear]]: | The speed of an aetheric beam is the transfer speed of its magnetic field, therefore both the speed and magnetic fields have a lot in common. In particular, both fields of a rotating beam have a common axis of rotation, so the [[wikipedia:Curl (mathematics)|curls]] of these fields are [[wikipedia:Collinearity|collinear]]: | ||
:<math>\boxed{curl\mathbf{\overrightarrow{B}}=curl\;k\mathbf{\overrightarrow{v}}\;\;\;\;\;\;\;grad\;k\cdot curl\mathbf{\overrightarrow{v}}=0}\label{collinear_rot_v_B}</math> | :<math>\boxed{curl\mathbf{\overrightarrow{B}}=curl\;k\mathbf{\overrightarrow{v}}\;\;\;\;\;\;\;grad\;k\cdot curl\mathbf{\overrightarrow{v}}=0}\label{collinear_rot_v_B}</math> | ||
| − | The magnetic forces are related to a warp of the aetheric beams, which are affected by the shear forces of | + | The magnetic forces are related to a warp of the aetheric beams, which are affected by the shear forces of surrounding pressure. The pressure gradient force, according to the density definition ([[Mass and inertia#Eq-2|"Mass and inertia", 2]]), is: |
:<math>\rho=\varepsilon_0 B^2\label{magnetic_force_1}</math> | :<math>\rho=\varepsilon_0 B^2\label{magnetic_force_1}</math> | ||
:<math>\rho\mathbf{\overrightarrow{f}}=grad\frac{\rho v^2}{2}=\frac{\varepsilon_0}{2}(B^2 grad\;v^2+v^2 grad\;B^2)\label{magnetic_force_2}</math> | :<math>\rho\mathbf{\overrightarrow{f}}=grad\frac{\rho v^2}{2}=\frac{\varepsilon_0}{2}(B^2 grad\;v^2+v^2 grad\;B^2)\label{magnetic_force_2}</math> | ||
| − | This force is decomposed into the components by a known [[Physical field#Vector analysis formulas|vector analysis formula]] for | + | This force is decomposed into the components by a known [[Physical field#Vector analysis formulas|vector analysis formula]] for 3D space: |
:<math>\rho\mathbf{\overrightarrow{f}}=\rho(\mathbf{\overrightarrow{v}}\cdot\nabla)\mathbf{\overrightarrow{v}}+\rho\mathbf{\overrightarrow{v}}\times curl\mathbf{\overrightarrow{v}}+\varepsilon_0 v^2(\mathbf{\overrightarrow{B}}\cdot\nabla)\mathbf{\overrightarrow{B}}+\varepsilon_0 v^2\mathbf{\overrightarrow{B}}\times curl\mathbf{\overrightarrow{B}}\label{magnetic_force_3}</math> | :<math>\rho\mathbf{\overrightarrow{f}}=\rho(\mathbf{\overrightarrow{v}}\cdot\nabla)\mathbf{\overrightarrow{v}}+\rho\mathbf{\overrightarrow{v}}\times curl\mathbf{\overrightarrow{v}}+\varepsilon_0 v^2(\mathbf{\overrightarrow{B}}\cdot\nabla)\mathbf{\overrightarrow{B}}+\varepsilon_0 v^2\mathbf{\overrightarrow{B}}\times curl\mathbf{\overrightarrow{B}}\label{magnetic_force_3}</math> | ||
| − | The <math>(\mathbf{\overrightarrow{B}}\cdot\nabla)\mathbf{\overrightarrow{B}}</math> component is related to the [[Electricity|electric]] interaction and also to | + | The <math>(\mathbf{\overrightarrow{B}}\cdot\nabla)\mathbf{\overrightarrow{B}}</math> component is related to the [[Electricity|electric]] interaction and also to the dependence of optical bonding force of two parallel light waves on their phase shift [http://www.nature.com/nphoton/journal/v3/n8/abs/nphoton.2009.116.html].<br> |
| − | The <math>\mathbf{\overrightarrow{B}}\times curl\mathbf{\overrightarrow{B}}</math> component is related to the | + | The <math>\mathbf{\overrightarrow{B}}\times curl\mathbf{\overrightarrow{B}}</math> component is related to the magnetic interaction of vortical flows. |
| − | :<math>\ | + | As force, energy and mass are interrelated, the electromagnetic interaction between vortices produces an error of superposition of their beam densities: |
| − | The magnetic force | + | :<math>\rho_\Sigma=\Sigma\rho+\Delta\rho\label{magnetic_force_4}</math> |
| + | The magnetic force of a beam is expressed with the [[wikipedia:Speed of light|speed of light]] in vacuum (<math>c^2=1/\varepsilon_0\mu_0</math>) (in the SI): | ||
:<math>\rho\mathbf{\overrightarrow{f}}=\frac{v^2}{c^2}(curl\mathbf{\overrightarrow{H}})\times\mathbf{\overrightarrow{B}}\label{magnetic_force_5}</math> | :<math>\rho\mathbf{\overrightarrow{f}}=\frac{v^2}{c^2}(curl\mathbf{\overrightarrow{H}})\times\mathbf{\overrightarrow{B}}\label{magnetic_force_5}</math> | ||
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The beam speeds reach the speed of light within the material domain. | The beam speeds reach the speed of light within the material domain. | ||
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| − | + | The magnetic force is included into Euler’s equation for a [[Continuum|continuum]]. One of the known [[wikipedia:Magnetohydrodynamics|magneto-hydrodynamics]] equations for an ideal electrically conducting fluid (gas) is Euler's equation, where the magnetic force is [[wikipedia:Ampère's force law|Ampere's force]]: | |
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| − | The magnetic force is included into | + | |
:<math>\rho\frac{\partial\mathbf{\overrightarrow{v}}}{\partial t}+\rho(\mathbf{\overrightarrow{v}}\cdot\nabla)\mathbf{\overrightarrow{v}}+grad(P+U)=(curl\mathbf{\overrightarrow{H}})\times\mathbf{\overrightarrow{B}}\tag{9 - SI}</math> | :<math>\rho\frac{\partial\mathbf{\overrightarrow{v}}}{\partial t}+\rho(\mathbf{\overrightarrow{v}}\cdot\nabla)\mathbf{\overrightarrow{v}}+grad(P+U)=(curl\mathbf{\overrightarrow{H}})\times\mathbf{\overrightarrow{B}}\tag{9 - SI}</math> | ||
Revision as of 16:52, 27 May 2017
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The speed of an aetheric beam is the transfer speed of its magnetic field, therefore both the speed and magnetic fields have a lot in common. In particular, both fields of a rotating beam have a common axis of rotation, so the curls of these fields are collinear:
\[\boxed{curl\mathbf{\overrightarrow{B}}=curl\;k\mathbf{\overrightarrow{v}}\;\;\;\;\;\;\;grad\;k\cdot curl\mathbf{\overrightarrow{v}}=0}\tag{1}\]
The magnetic forces are related to a warp of the aetheric beams, which are affected by the shear forces of surrounding pressure. The pressure gradient force, according to the density definition ("Mass and inertia", 2), is:
\[\rho=\varepsilon_0 B^2\tag{2}\]
\[\rho\mathbf{\overrightarrow{f}}=grad\frac{\rho v^2}{2}=\frac{\varepsilon_0}{2}(B^2 grad\;v^2+v^2 grad\;B^2)\tag{3}\]
This force is decomposed into the components by a known vector analysis formula for 3D space:
\[\rho\mathbf{\overrightarrow{f}}=\rho(\mathbf{\overrightarrow{v}}\cdot\nabla)\mathbf{\overrightarrow{v}}+\rho\mathbf{\overrightarrow{v}}\times curl\mathbf{\overrightarrow{v}}+\varepsilon_0 v^2(\mathbf{\overrightarrow{B}}\cdot\nabla)\mathbf{\overrightarrow{B}}+\varepsilon_0 v^2\mathbf{\overrightarrow{B}}\times curl\mathbf{\overrightarrow{B}}\tag{4}\]
The \((\mathbf{\overrightarrow{B}}\cdot\nabla)\mathbf{\overrightarrow{B}}\) component is related to the electric interaction and also to the dependence of optical bonding force of two parallel light waves on their phase shift [1].
The \(\mathbf{\overrightarrow{B}}\times curl\mathbf{\overrightarrow{B}}\) component is related to the magnetic interaction of vortical flows.
As force, energy and mass are interrelated, the electromagnetic interaction between vortices produces an error of superposition of their beam densities:
\[\rho_\Sigma=\Sigma\rho+\Delta\rho\tag{5}\]
The magnetic force of a beam is expressed with the speed of light in vacuum (\(c^2=1/\varepsilon_0\mu_0\)) (in the SI):
\[\rho\mathbf{\overrightarrow{f}}=\frac{v^2}{c^2}(curl\mathbf{\overrightarrow{H}})\times\mathbf{\overrightarrow{B}}\tag{6}\]
| Domain | SI | CGS | Simplified | \(\tag{7}\) |
|---|---|---|---|---|
| Vacuum (aether) | \[\rho\mathbf{\overrightarrow{f}}=\frac{v^2}{c^2}(curl\mathbf{\overrightarrow{H}})\times\mathbf{\overrightarrow{B}}\] | \[\rho\mathbf{\overrightarrow{f}}=\frac{v^2}{4\pi c^2}(curl\mathbf{\overrightarrow{H}})\times\mathbf{\overrightarrow{B}}\] | \[\rho\mathbf{\overrightarrow{f}}=v^2(curl\mathbf{\overrightarrow{B}})\times\mathbf{\overrightarrow{B}}\] | |
| Matter | \[\rho\mathbf{\overrightarrow{f}}=(curl\mathbf{\overrightarrow{H}})\times\mathbf{\overrightarrow{B}}\] | \[\rho\mathbf{\overrightarrow{f}}=\frac{1}{4\pi}(curl\mathbf{\overrightarrow{H}})\times\mathbf{\overrightarrow{B}}\] | \[\varepsilon\rho\mathbf{\overrightarrow{f}}=c^2(curl\mathbf{\overrightarrow{H}})\times\mathbf{\overrightarrow{B}}\] | \(\tag{8}\) |
The beam speeds reach the speed of light within the material domain.
The magnetic force is included into Euler’s equation for a continuum. One of the known magneto-hydrodynamics equations for an ideal electrically conducting fluid (gas) is Euler's equation, where the magnetic force is Ampere's force: \[\rho\frac{\partial\mathbf{\overrightarrow{v}}}{\partial t}+\rho(\mathbf{\overrightarrow{v}}\cdot\nabla)\mathbf{\overrightarrow{v}}+grad(P+U)=(curl\mathbf{\overrightarrow{H}})\times\mathbf{\overrightarrow{B}}\tag{9 - SI}\]
See also
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