# Magnetism

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: $\boxed{curl\;\mathbf{\overrightarrow{B}}=k\;curl\;\mathbf{\overrightarrow{v}}}\tag{1}$ 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 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: $\rho\frac{\partial\mathbf{\overrightarrow{v}}}{\partial t}+\rho(\mathbf{\overrightarrow{v}}\cdot\nabla)\mathbf{\overrightarrow{v}}+grad(P+U)=(curl\;\mathbf{\overrightarrow{H}})\times\mathbf{\overrightarrow{B}}\tag{9 - SI}$