# Electricity

Corresponding Wikipedia article: Electric field

## Definition

The electric field is not a basic parameter of the aether state, but this is a force field, which exists relatively to the affected objects.

Comparative summary of the electric and magnetic fields
Field
Electrical Magnetic
Source The magnetized aether and the motion or variation of the magnetic field over time. Undefined.
Manifestation Force, which affects the electrically charged aetheric vortices. Force, density.
Reference frame Depends on frame, if the force is caused by a motion. Independent.
Spatial dimensionality At least 3, which is required for the vortices. At least 2.

The electric force is separated from the magnetic force ("Magnetism", 6) by separating its fraction from the total magnetic field: $\mathbf{\overrightarrow{B}}=curl\;k\mathbf{\overrightarrow{v}}\;\;\;\;\;\;k=const$ Under this condition, the vectors $$\mathbf{\overrightarrow{B}}$$ and $$(curl\mathbf{\overrightarrow{B}})$$, are collinear according to a property ("Magnetism", 1), so the magnetic force is zero. The value and sign of electric charge depends on the $$k$$ value. In order to determine the $$k$$ and force (energy) values, the mass density$$\rho$$ should be included into the equation. The equations, which are consistent with the known electromagnetism laws, are the following:

 SI CGS Simplified $$\tag{1}$$ $\rho\mathbf{\overrightarrow{v}}=-q\mathbf{\overrightarrow{A}}$ $\rho\mathbf{\overrightarrow{v}}=-\frac{q}{c}\mathbf{\overrightarrow{A}}$ $\varepsilon\rho\mathbf{\overrightarrow{v}}=-q\mathbf{\overrightarrow{A}}$ $\mathbf{\overrightarrow{B}}=curl\mathbf{\overrightarrow{A}}$ $$\tag{2}$$

$$\mathbf{\overrightarrow{A}}$$ is a magnetic potential vector;
$$q$$ is a volumetric density of electric charge;
$$\varepsilon$$ is a relative permittivity of the medium ($$\varepsilon=1$$ for the vacuum);
$$c$$ is a speed of light in vacuum.

The magnetic potential is the only source of electric field: $\rho\mathbf{\overrightarrow{f}}=-q\frac{\mathrm{d}\mathbf{\overrightarrow{A}}}{\mathrm{d}t}\tag{3 - SI}$ $\rho\mathbf{\overrightarrow{f}}=-\frac{q}{c}\frac{\mathrm{d}\mathbf{\overrightarrow{A}}}{\mathrm{d}t}\tag{3 - CGS}$ $\varepsilon\rho\mathbf{\overrightarrow{f}}=-q\frac{\mathrm{d}\mathbf{\overrightarrow{A}}}{\mathrm{d}t}\tag{3 - Sim.}$ The magnetic field derivative with respect to time is decomposed as a material derivative but with an additional term: $\frac{\mathrm{d}\mathbf{\overrightarrow{B}}}{\mathrm{d}t}=\frac{\partial\mathbf{\overrightarrow{B}}}{\partial t}+(\mathbf{\overrightarrow{v}}\cdot\nabla)\mathbf{\overrightarrow{B}}-(\mathbf{\overrightarrow{B}}\cdot\nabla)\mathbf{\overrightarrow{v}}\tag{4}$ The term $$-(\mathbf{\overrightarrow{B}}\cdot\nabla)\mathbf{\overrightarrow{v}}$$ expresses that deceleration of a beam compresses it (increases $$\mathbf{\overrightarrow{B}}$$), and acceleration rarefies it (decreases $$\mathbf{\overrightarrow{B}}$$).

The electric field is divided into two components with different causes of the forces:

Field Cause Law
Electrostatic
(potential, conservative)
Magnetized aether motion.

$(\mathbf{\overrightarrow{v}}\cdot\nabla)\mathbf{\overrightarrow{B}}-(\mathbf{\overrightarrow{B}}\cdot\nabla)\mathbf{\overrightarrow{v}}\neq 0$

Lorentz and Ampere force
Vortical
(dynamic)
Magnetic flux variation.

$\frac{\partial\mathbf{\overrightarrow{B}}}{\partial t}\neq 0$

The formula of electrostatic field, which is produced by a moving charge $$q$$ with respect to the source of permanent magnetic field $$\mathbf{\overrightarrow{B}}$$ at velocity $$\mathbf{\overrightarrow{v}}$$, is: $\rho\mathbf{\overrightarrow{f}}=q\mathbf{\overrightarrow{v}}\times\mathbf{\overrightarrow{B}}\tag{5 - SI}$ $\rho\mathbf{\overrightarrow{f}}=q\frac{\mathbf{\overrightarrow{v}}}{c}\times\mathbf{\overrightarrow{B}}\tag{5 - CGS}$ $\varepsilon\rho\mathbf{\overrightarrow{f}}=q\mathbf{\overrightarrow{v}}\times\mathbf{\overrightarrow{B}}\tag{5 - Sim.}$ The proof of (5) is reduced to the proof of equation: $\mathbf{\overrightarrow{v}}\times\mathbf{\overrightarrow{B}}=-\frac{\mathrm{d}\mathbf{\overrightarrow{A}}}{\mathrm{d}t}\tag{6}$ Since the field $$\mathbf{\overrightarrow{A}}$$ is potential only at $$\mathbf{\overrightarrow{B}}=0$$, the equality (6) can be replaced by the equality of curls: $curl(\mathbf{\overrightarrow{v}}\times\mathbf{\overrightarrow{B}})=-curl\;\frac{\mathrm{d}\mathbf{\overrightarrow{A}}}{\mathrm{d}t}=-\frac{\mathrm{d}\mathbf{\overrightarrow{B}}}{\mathrm{d}t}=-(\mathbf{\overrightarrow{v}}\cdot\nabla)\mathbf{\overrightarrow{B}}+(\mathbf{\overrightarrow{B}}\cdot\nabla)\mathbf{\overrightarrow{v}}\tag{7}$ Also, according to the known identity, which is applicable to 3-dimensional space: $curl(\mathbf{\overrightarrow{v}}\times\mathbf{\overrightarrow{B}})=(div\;\mathbf{\overrightarrow{B}}+\mathbf{\overrightarrow{B}}\cdot\nabla)\mathbf{\overrightarrow{v}}-(div\mathbf{\overrightarrow{v}}+\mathbf{\overrightarrow{v}}\cdot\nabla)\mathbf{\overrightarrow{B}}\tag{8}$ Since the magnetic field is vortical ($$div\;\mathbf{\overrightarrow{B}}=0$$), and the velocity field consists of the vortical and/or uniform components ($$div\mathbf{\overrightarrow{v}}=0$$), the formula (5) is proven.