Magnetic energy
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Corresponding Wikipedia article: Magnetic energy
The magnetic interaction of the aetheric vortices is the magnetic force ("Magnetism", 7 and 8) effect, which manifests the interaction potential energy, which tends to its minimum.
It can be written similar to the equation ("Magnetism", 4): \[grad\frac{\mathbf{\overrightarrow{B}}\mathbf{\overrightarrow{H}}}{2}=(\mathbf{\overrightarrow{B}}\cdot\nabla)\mathbf{\overrightarrow{H}}+\mathbf{\overrightarrow{B}}\times curl\mathbf{\overrightarrow{H}}\tag{1}\] The \((\mathbf{\overrightarrow{B}}\cdot\nabla)\mathbf{\overrightarrow{H}}\) component produces the electric field, and it is zero for the magnetic field. The \((\mathbf{\overrightarrow{B}}\times curl\mathbf{\overrightarrow{H}})\) component is the magnetic force within matter.
| SI | CGS | Simplified | \(\tag{2}\) |
|---|---|---|---|
| \[w_B=\frac{\mathbf{\overrightarrow{B}}\mathbf{\overrightarrow{H}}}{2}=\frac{|\mathbf{\overrightarrow{B}}|^2}{2\mu_0 \mu}\] | \[w_B=\frac{\mathbf{\overrightarrow{B}}\mathbf{\overrightarrow{H}}}{8\pi}=\frac{|\mathbf{\overrightarrow{B}}|^2}{8\pi\mu}\] | \[w_B=\frac{\mathbf{\overrightarrow{B}}\mathbf{\overrightarrow{H}}c^2}{2}=\frac{|\mathbf{\overrightarrow{B}}|^2c}{2\mu}\] |
Let the first source has the field \(\mathbf{\overrightarrow{B_1}}\) and \(\mathbf{\overrightarrow{H_1}}\), and the second has \(\mathbf{\overrightarrow{B_2}}\) and \(\mathbf{\overrightarrow{H_2}}\). Then the equation of full energy is: \[\frac{(\mathbf{\overrightarrow{B_1}}+\mathbf{\overrightarrow{B_2}})(\mathbf{\overrightarrow{H_1}}+\mathbf{\overrightarrow{H_2}})}{2}=\frac{\mathbf{\overrightarrow{B_1}}\mathbf{\overrightarrow{H_1}}}{2}+\frac{\mathbf{\overrightarrow{B_1}}\mathbf{\overrightarrow{H_2}}+\mathbf{\overrightarrow{B_2}}\mathbf{\overrightarrow{H_1}}}{2}+\frac{\mathbf{\overrightarrow{B_2}}\mathbf{\overrightarrow{H_2}}}{2}\tag{3}\] Here \(\frac{\mathbf{\overrightarrow{B_1}}\mathbf{\overrightarrow{H_1}}}{2}\) and \(\frac{\mathbf{\overrightarrow{B_2}}\mathbf{\overrightarrow{H_2}}}{2}\) are the densities of own energy for the first and the second source separately. The interaction energy density with certain permeability \(\mu\) at the given point has few identical representations: \[\frac{\mathbf{\overrightarrow{B_1}}\mathbf{\overrightarrow{H_2}}+\mathbf{\overrightarrow{B_2}}\mathbf{\overrightarrow{H_1}}}{2}=\mu_0\mu\mathbf{\overrightarrow{H_1}}\mathbf{\overrightarrow{H_2}}=\mathbf{\overrightarrow{B_1}}\mathbf{\overrightarrow{H_2}}=\mathbf{\overrightarrow{H_1}}\mathbf{\overrightarrow{B_2}}\tag{4}\] Thus the potential energy volumetric density of the magnetic interaction is: \[w=\mathbf{\overrightarrow{B}}\mathbf{\overrightarrow{H}}\tag{5}\]
Example. The inductive coil has the field energy of density \(\mathbf{\overrightarrow{B}}\mathbf{\overrightarrow{H}}/2\) and interacts with the magnetized core with the energy density \(\mathbf{\overrightarrow{B}}\mathbf{\overrightarrow{H}}\), which produces the heat losses.
Two magnetic object (which have a magnetic field) are mutually attracted by their poles by some way, which provides the minimal energy of the resulting field:
| Attraction of poles | Examples |
|---|---|
| different | Solid bodies (magnets). Rarely the elementary particles. |
| same | Pairs of elementary particles, the covalent bonds or the Cooper pairs. |
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