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<p class="art-type" id="articleinfo">
Opinion Article</p>
<p class="art-title">
Foundation of Electrodynamics</p>
<p class="art-author"><?php $authors="
Branko V. Miskovic"; echo (stristr($authors,$coauthor))?str_replace($coauthor,"<a href='".$extpath."authors/".$courl."' target='_blank'>".$coauthor."</a>",$authors):$authors; ?></p>
<p class="art-affl">
Independent Scientist, Novi Sad, Serbia</p>
<p class="art-aff"><b>*Corresponding author: <?php $corresponding_author="
Branko V. Miskovic"; echo ($coauthor!="" && $coauthor==$corresponding_author)?"<a href='".$extpath."authors/".$courl."' target='_blank'>".$coauthor."</a>":$corresponding_author;?></b>,
Independent Scientist,
Atar 16, 21209 Bukovac, Novi Sad,
Serbia,
E-mail: <a href="mailto:brankovmiskovic@yahoo.com">brankovmiskovic@yahoo.com</a></p>
<p class="art-aff"><b>Received:</b> September 18, 2023
<b>Accepted:</b> October 17, 2023
<b>Published:</b> October 25, 2023</p>
<p class="art-aff"><b>Citation:</b> Miskovic BV. Foundation of
Electrodynamics. <i>Int J Phys Stud Res</i>. 2023;
4(1): 98-103.
doi: <a href="https://doi.org/10.18689/ijpsr-1000116">10.18689/ijpsr-1000116</a></p>
<p class="art-aff"><b>Copyright:</b> &copy; 2023 The Author(s). This work
is licensed under a Creative Commons
Attribution 4.0 International License, which
permits unrestricted use, distribution, and
reproduction in any medium, provided the
original work is properly cited.</p>
<p><a href="<?php echo $extpath;?><?php echo $jres['journal_link'];?>/ijpsr-1000116.pdf" class="btn btn-danger pull-right" target="_blank">Download PDF</a></p>
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<div class="articlecontent">
<p class="art-subhead" id="abstract">Abstract</p>
<p class="art-para">EM theory started from electricity and its current, as the carriers or objects, mediated
by the fields and potentials. In the opposite sense, the fields are formal features of the
potentials, limited by the carriers. Apart from the central Coulomb&#8217;s law, similar
Ampere&#8217;s law is here generalized. The radial &#8211; static and transverse &#8211; kinetic, are thus
supplemented by longitudinal &#8211; dynamic forces. The fields are introduced in the three
ways: as the evident forces, via the object densities and by analogy of the potentials with
fluid mechanics. As the simplest basic set, the two algebraic relations of J. J. Thomson
operate by the two moving fields. Instead of the parallel or hierarchical processes, they
form a causal loop with the constitutive field relations. The spatial derivatives of the
algebraic pair give the four differential forms, wider from Maxwell&#8217;s equations. The
elimination of excessive, and explanation of remaining terms, convincingly relate the
two sets. Maxwell&#8217;s equations are finally presented in Einstein&#8217;s tensor form, concerning
4D space.</p>
<p class="art-para"><b>Keywords:</b> Field, Potential, Static, Kinetic, Dynamic</p>
<p class="art-subhead" id="intro">Introduction</p>
<p class="art-para">
By analogy with gravitation, EM theory formerly started by Coulomb&#8217;s law for static
interaction of two electric charges. The similar Ampere&#8217;s law, for magnetic interaction of
two moving charges, as the elementary currents, has not been formulated in general. Its
special case is restricted to the transverse plane containing the two charges, and moving
with them. Even as such, it is successfully applied to the line conductors and their fields.
Its application to the oblique position of a moving dipole implies the torque acting on
this dipole. Not only that such torque has never been practically confirmed, but is
theoretically doubtful. Without the general Ampere&#8217;s law &#8211; merely here completed, EM
theory demanded some other formal approaches.</p>
<p class="art-para">
Fluid mechanics generalized Newtonian laws from discrete to distributed quantities.
Instead of such inductive development, EM field theory is founded by analogy, on the
basis of Maxwell&#8217;s set, intuitively derived from the technical practice. As the new
mathematics and its abstract application were not habituated by the contemporaries,
this Maxwell&#8217;s challenge was difficult to understand and accept. From his set Maxwell
derived the known wave equation, thus predicting EM waves. Hertz&#8217; empirical verification
of these waves, with some arrangement of the equations, was sufficient for the wide
acceptance of Maxwell&#8217;s theory, without insight into the essence.</p>
<p class="art-para">
In the meantime, J. J. Thomson proposed the considerably simpler and logically
clearer pair of algebraic relations, treating the field motions &#8211; instead of their variations.
Despite the smaller number of the simpler equations, there was difficult to follow the
motions of invisible fields, unlike their variations accessible by the resting instruments,
at the typical points at least. Not elaborated in practice, Thomson&#8217;s relations have been
suppressed by Hertz&#8217; affirmation of Maxwell&#8217;s theory. Only L. Landau presented them,

but without any discussion. The other expositions of EM
theory do not even this. On the other hand, these relations
are the basis of the transformations of the fields and
coordinates, obeying the formal invariance of Maxwell&#8217;s set.</p>
<p class="art-para">
At least some of differential equations have their algebraic
equivalences. The particular inductive procedures consist of
the original hits, without a general approach strictly
elaborated. For 150 years of Maxwell&#8217;s equations, there is
unknown any attempt of their algebraic resolution. The
special technical situations are successfully treated by
computers. However, the application of the two differential
operations to Thomson&#8217;s pair gives the four differential forms,
wider from Maxwell&#8217;s set. By elimination of the excessive, with
explanation of other terms, this job is here finalized. The
formal procedures further illuminate the serious physical
relations. The indirect inductive approach to this matter is
already presented in the references.</p>
<p class="art-subhead">
EM Fields</p>
<p class="art-para">
The application of the relativity principle and convective
field derivatives enable the consistent foundation of EM
theory. These two concepts can be commonly presented:</p>
<div class="art-img" id="e001">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e001.gif" class="img-responsive center-block"/></div>
<p class="art-para">
Here v is the object speed, and V &#8211; that of the field A. The
vector field gradient, as the tensor, multiplied by the vector
also gives the vector. The object motion causes relative, but
that of the field gives the opposite, convective field variations,
each of them proportional with the field gradient. The spatial
motions and temporal variations are thus related.
EM theory has been founded on electricity (q), as the
abstract bipolar substance. Its volume density gives the scalar
field, Q = &#8706;q/&#8706;v, forming respective current: J = VQ. Its
divergence gives the continuity equation (2). Owing to the
inert particles, their free motion is uniform, without
acceleration or the speed divergence. The former term thus
annuls, and latter one, as the convective field derivative, gives
the temporal variations</p>
<div class="art-img" id="e002">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e002.gif" class="img-responsive center-block"/></div>
<p class="art-para">
Faraday had introducing the force fields empirically, by
the torques (3) and force differences (4) affecting respective
dipoles. Though not immediately formulated, these equations
adequately express the direct empirical impressions. Electric
or magnetic dipoles, directed by the torques (3) along the
fields, present the abstract field lines, as the force directions.
Thus oriented dipoles are drawn into the stronger fields (4).</p>
<div class="art-img" id="e003">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e003.gif" class="img-responsive center-block"/></div>
<div class="art-img" id="e004">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e004.gif" class="img-responsive center-block"/></div>
<p class="art-para">
The symmetry of these equations gives the impression of
the parallel electric and magnetic phenomena. However,
unlike an electric dipole (p = ql), as the polar vector determined
by two opposite poles separated by a distance (l), the
magnetic dipole or moment (m) cannot be anyhow resolved.
Though predicted by analogy, the free magnetic poles have
never been separated, but the division of one, ever gives the
two shorter dipoles. However, the rotation of an electric
dipole around one its pole gives the magnetic moment, as the
axial vector, m = p &#215; v, announcing the hierarchy of EM
phenomena. The circular electric currents carry toroidal
magnetic fields, or vice versa.</p>
<p class="art-para">
The field of an electric dipole starts from its positive, and
terminates on the negative poles. The medium disturbance,
as the global field integral, is opposite to the dipole: d = &#8211; p.
The electric dipoles thus orient against external fields, and
these fields are usually weaker at material media. However,
the magnetic field of a current contour is opposite inside and
outside this contour. The magnetic disturbance, h = m, is
added to the external field, thus increasing it at matter. This is
the evident asymmetry of the two EM phenomena.</p>
<p class="art-para">
By volume densities of the dipoles or medium
disturbances, Maxwell introduced the rational fields, e.g.
polarization (P) and displacement of electricity (D). Such fields
are related by (5), and these with the force fields &#8211; by (6).</p>
<div class="art-img" id="e005">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e005.gif" class="img-responsive center-block"/></div>
<div class="art-img" id="e006">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e006.gif" class="img-responsive center-block"/></div>

<p class="art-para">
The relative electric and magnetic factors (<sub>r</sub>
) relate the
total and vacuum field components, but respective vacuum
factors (<sub>o</sub>) dimensionally reconcile the two field types being
independently introduced. The dimensionless relative factors
equal to units at the space without matter. The equivalent
vacuum medium, of the unknown essence and structure, had
been also understood. Its negation in modern physics fails in
any interpretation of EM fields and respective waves. The
newer similar notions, as the quantum or Higgs&#8217; field, are also
equally abstract.</p>
<p class="art-para">
The vertical substitutions of the field difference and sum
give the two constitutive relations (7), hiding the field
asymmetry. In each of them, respective total field is
proportional with its vacuum component, via the total
constants. However, the former relation expresses the rational
over respective force fields, just oppositely to the latter of
them.</p>
<div class="art-img" id="e007">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e007.gif" class="img-responsive center-block"/></div>
<p class="art-para">
Instead of the symmetry or hierarchy, these equations
point to a causal loop, as the field relations. Missing the
middle phase of this consideration, consisting of (5) & (6),
these two equations further enhance the impression of
symmetry, announced by (3) & (4). The two EM constants in
the basic sets, instead of a field pair, further hide the essential
asymmetry.</p>
<p class="art-subhead">

Algebraic Relations</p>
<p class="art-para">
Instead of Maxwell&#8217;s differential equations, we here start
with Thomson&#8217;s algebraic relations (8), as the simplest basic
set. Here V is the speed of electric, and U &#8211; of magnetic fields.
At least for their distinction, the former relation we call kinetic,
but latter dynamic one. Namely, latter of them modifies the
motion expressed by the former. In both of them, the motion
of one total, represents or produces the other vacuum fields.
The former relation operates by the rational, but latter by
force fields. The opposite orders of the fields and speeds, in
the cross-products, express their essential asymmetry.</p>
<div class="art-img" id="e008">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e008.gif" class="img-responsive center-block"/></div>
<p class="art-para">
The kinetic relation links the vector densities of the two
medium disturbances. However, applied to a rotating electric,
it would give the infinite magnetic fields, as the unacceptable
result. For this reason, it has been ignored.</p>
<p class="art-para">
The dynamic relation describes respective induction,
noticed empirically. A magnet moving with its field causes the
electric induction in the field domain. It is also applicable to
the rotating magnetic field, as the sum of the resting periodical
components. In practice, it is usually added (9) to the
equivalent kinetic field (10), affecting moving electricity:</p>
<div class="art-img" id="e009">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e009.gif" class="img-responsive center-block"/></div>
<div class="art-img" id="e010">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e010.gif" class="img-responsive center-block"/></div>
<p class="art-para">
Here v is the object speed, and U &#8211; that of the field. The
principle of relativity is thus understood, concerning the
mutual motion of the object and field. In this manner, the
dynamic Thomson&#8217;s relation has been also hidden.</p>
<p class="art-para">
The algebraic pairs (7) & (8) form the causal loop (Fig 1).
The two asymmetries supplement each other. EM theory thus
appears as a closed scientific system, operating by the two
field pairs, irrespective of any material carriers.</p>
<div class="art-img" id="f001">
<img src="<?php echo $imgpath;?>images/ijpsr-116-f001.gif" class="img-responsive center-block"/></div>
<p class="art-para">

According to Maxwell&#8217;s & Einstein&#8217;s relations (11),
Pointing&#8217;s cross-products of the vacuum or total fields relate
the moving densities of the energy and mass (12).</p>
<div class="art-img" id="e011">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e011.gif" class="img-responsive center-block"/></div>
<div class="art-img" id="e012">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e012.gif" class="img-responsive center-block"/></div>

<p class="art-para">
At a free space without explicit matter, the two relative
factors equal to units, and the propagation reaches the
vacuum wave speed: c<sub>o</sub><sup>
2</sup>
 = 1/e<sub>o</sub>m<sub>o</sub>. With respect to the relative
factors &#8211; in principle greater from units, the effective speed
through matter is usually smaller. In some special cases, of so
called dispersive media, this ratio may be inverse one.</p>
<p class="art-para">
In comparison with sound and other known waves, the
two constants look alike structural elasticity (e) and mass
density (m). With respect to the vacuum factors, some medium
&#8211; enabling EM waves, is unavoidable. Though the explicit
matter predominates inside massive bodies, this medium is
omnipresent throughout the cosmic space, thus possibly
explaining the predominance of the implicit matter, in cosmos
as a whole.</p>
<p class="art-subhead">
Central Forces</p>
<p class="art-para">
The application of (8a) to the central electric field (13a) of
a moving electric charge (q) gives respective magnetic field
(13b). Avoiding the problematic kinetic relation, this result is
obtained by the integration along a line conductor. The
kinetic force (10), affecting the electricity moving through
magnetic field, gives the special case of Ampere&#8217;s law (14).</p>
<div class="art-img" id="e013">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e013.gif" class="img-responsive center-block"/></div>
<div class="art-img" id="e014">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e014.gif" class="img-responsive center-block"/></div>
<p class="art-para">
This force is here formally resolved into its axial and radial
components. Unlike the former component stretching the
particle, the latter of them tends to the radial compression.
However, their ellipsoidal sum gives the unacceptable torque
on a moving electric dipole, not practically confirmed. The
opposite axial forces mutually cancel along the line
conductors, and this equation then gives the acceptable
results.</p>
<p class="art-para">
The reference of the object speed may be irrelevant: owing
to the magnetic field carried by respective conductor, the
relative and absolute speeds are equal. However, in the general
case (15), the absolute speed need be substituted by relative
one (v &#8211; U), thus also applying the dynamic relation (8b).</p>
<div class="art-img" id="e015">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e015.gif" class="img-responsive center-block"/></div>
<p class="art-para">
However, the magnetic field motion around a punctual
charge is problematic. Its rest or motion with the particle would
cancel the magnetic force or produce the cumulative sequence

of EM processes (8), both equally unacceptable. There remains
a possibility of its transverse motion (16a). The zero axial force
is satisfied by (16b), where the conditional equality concerns
the common motion of the carrier and object.</p>
<div class="art-img" id="e016">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e016.gif" class="img-responsive center-block"/></div>
<p class="art-para">
The regular equality is expressible in the scalar forms (17),
where &#952; is the polar angle. The transverse convective derivative
applied to the central potential (38a) &#8211; on Fig 2, gives the
same result. With respect to the magnetic field independent
of its own objects, this result is general. At least effectively,
the circular field lines expand in the front, and shrink behind
the particle, with the instantaneous rest in the equatorial
plane. In this position, the result (14) is also valid. The
conditions (16) substituted into (15) finally give the general
Ampere&#8217;s law (18).</p>
<div class="art-img" id="f002">
<img src="<?php echo $imgpath;?>images/ijpsr-116-f002.gif" class="img-responsive center-block"/></div>
<p class="art-para">

The two sine terms present the kinetic forces (14). The third
term expresses the axial dynamic induction, due to the transverse
field expansion or shrink. In fact, the medium is compressed and
accelerated &#8211; in the front, and vice versa behind the particle. The
induction law (40) applied to the convective derivative of (38b)
just expresses this. At common motion of the two charges the
first term annuls, reducing (18) to (19).</p>
<div class="art-img" id="e019">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e019.gif" class="img-responsive center-block"/></div>
<p class="art-para">
The kinetic forces do not affect resting electricity.
Therefore, the dynamic induction subtracted from the central
static field (20a) gives the ellipsoidal result on a resting
instrument, irrespective of the even pressure upon the moving
carrier. At the common motion, with sin2
&#952; + cos2
&#952; = 1, the
central force (20b) excludes the torque on a moving dipole.</p>
<div class="art-img" id="e019">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e020.gif" class="img-responsive center-block"/></div>
<div class="art-img" id="e019">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e021.gif" class="img-responsive center-block"/></div>
<p class="art-para">
At least some of differential equations have their algebraic
The total force (21), affecting a moving charge, thus
consists of the static, kinetic and dynamic components. This
central sum tends to naught approaching the speed c, just
while the mass of the particle is growing into infinity.</p>
<p class="art-subhead">

Differential Equations</p>
<p class="art-para">

The two algebraic relations operate by the two EM fields,
but differential equations &#8211; by their spatial and temporal
derivatives. Therefore, the differential analysis of the former is
the way for its relation with latter sets. In this sense, the
routine application of the operation divergence to the
algebraic pair gives the two following differential forms:</p>
<div class="art-img" id="e019">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e022.gif" class="img-responsive center-block"/></div>
<div class="art-img" id="e019">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e023.gif" class="img-responsive center-block"/></div>
<p class="art-para">
Without the speed derivatives, these forms are comparable
with respective Maxwell&#8217;s equations (24) & (25), thus restricted
to the two homogeneous speeds, at the stationary EM
processes. This formal condition just points to the field inertia,
so far being ascribed to their material carriers.</p>
<div class="art-img" id="e019">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e024.gif" class="img-responsive center-block"/></div>
<div class="art-img" id="e019">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e025.gif" class="img-responsive center-block"/></div>
<p class="art-para">
The middle expressions represent the scalar fields. The
axial motion of a circular field vortex forms the sources of the
other EM field. In the absence of such electric vortex (24)
turns into the trivial equation, expressing the closed field lines
and excluding the existence of free magnetic poles.</p>
<p class="art-para">
The electric field terminals, in the static equation (25),have
been understood as the charge density: Q = &#8706;q/&#8706;v. Alike a
black hole affecting surrounding stars, a charge particle is
expected in the center of the radial electric field. Therefore, its
reality is founded on the spatial location, unlike magnetic
poles which cannot be even located in space. A central static
field may be understood as the dynamic induction (8b) at the
axial motion of circular magnetic vortices along t-axis.</p>
<p class="art-para">
On the other hand, the operation curl applied to the
algebraic pair (8) gives (26) & (27). The terms with the speed
derivatives are here already missed. The middle field
divergences may be substituted by the two above equations.
The two remaining terms, as the convective field derivatives,
give the opposite &#8211; temporal field variations. The magnetic
vortices, in the kinetic equation (26), embrace electric currents,
as the motion of free and/or bound electricity. Similar electric
vortex, in the dynamic equation (27), acts along the variable
current, against possible acceleration of the moving electricity.</p>
<div class="art-img" id="e026">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e026.gif" class="img-responsive center-block"/></div>
<div class="art-img" id="e0277">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e027.gif" class="img-responsive center-block"/></div>
<p class="art-para">

Thus completed Maxwell&#8217;s set, missing the speed
derivatives, is restricted to the stationary processes. With
respect to the magnetic &#8211; produced by moving electric fields
(8a), the acceleration of electricity is taken into account.</p>
<p class="art-para">
The diagram (Fig. 3) presents the differential causal relations.
The initial asymmetry of Thomson&#8217;s pair is here increased by the
different realities of the electric and magnetic charges.</p>

<div class="art-img" id="f003">
<img src="<?php echo $imgpath;?>images/ijpsr-116-f003.gif" class="img-responsive center-block"/></div>

<p class="art-para">The separation of the static from dynamic electric fields is
presented by the feedback on the main causal loop. It
expresses the formal production of electricity, as the apparent
field carriers. Starting from the electricity assumed in advance,
EM theory has been treated as the open scientific system.</p>
<p class="art-subhead">
Tensor Forms</p>
<p class="art-para">
Einstein condensed Maxwell&#8217;s set into the two tensor
forms, describing the 4D relations. Unlike his indirect procedure
&#8211; via EM potentials, the direct transfer is more transparent at
least. In this aim, Maxwell&#8217;s set is a little accommodated
(28)&#247;(31). The free electricity &#8211; moving from the past into future
&#8211; represents the fourth current component (28). The temporal
field derivatives, as the gradients along the metrical t-axis, are
replaced to the left of (29) & (31). Each of these vector equations
is resolvable into the scalar triples. The two subsets, of the four
equations each, are expressible by the two tensor forms (32).</p>

<div class="art-img" id="e028">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e028.gif" class="img-responsive center-block"/></div>
<div class="art-img" id="e029">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e029.gif" class="img-responsive center-block"/></div>
<div class="art-img" id="e030">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e030.gif" class="img-responsive center-block"/></div>
<div class="art-img" id="e031">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e031.gif" class="img-responsive center-block"/></div>
<div class="art-img" id="e032">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e032.gif" class="img-responsive center-block"/></div>
<p class="art-para">The left form operates by the rational, as the products of
the charge density with kinematical quantities, but right one
&#8211; by the force fields, possibly introduced from potentials (35b)
& (37a). The tensor terms are thus determined:</p>
<div class="art-img" id="e033">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e033.gif" class="img-responsive center-block"/></div>
<div class="art-img" id="e034">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e034.gif" class="img-responsive center-block"/></div>
<p class="art-para">

The index i = (t, x, y, z) here denotes the ordinal numbers of
the equations in the subsets, and the sums concern the index j
&#8800; i. The two field pairs seem to be inversely related with variation
of a spatial distance. Therefore, one of them has been treated as
covariant, and other &#8211; as contra-variant vectors. However, owing
to the medium disturbances usually proportional with respective
forces, this apparent distinction is excessive.</p>
<p class="art-para">
With the metrical sense of temporal axis, in (29) & (31), the
natural units (&#949;<sub>o</sub>
 = 1 = &#956;<sub>o</sub>
) are here understood. Einstein used, at
his time actual, units of Heaviside (&#949;<sub>o</sub>
 = 1/c = &#956;<sub>o</sub>
), with the
factor1/c in the two first columns. Their opposite signs, following
from the initial asymmetry of (8), substituted by imaginary unit,
as the average, ascribe the imaginary sense to t-axis</p>
<p class="art-subhead">
EM Potentials</p>
<p class="art-para">
In the fluidic model, the static force opposite to the
energy gradient equals to the fluid pressure, as the energy
density (35a). Respective field, as the specific force, is equally
related with the potential, as the specific energy (35b).</p>
<div class="art-img" id="e035">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e035.gif" class="img-responsive center-block"/></div>
<p class="art-para">
Carried by electric current (J = VQ), the moving static just
forms respective kinetic potentials (36a). Unlike the electricity
and its current, being directly related, the two potentials are
mediated by EM constants. Apart from the static pressure (&#934;),
the disturbance depends on the medium elasticity (e), as well
as the moving mass &#8211; on its own density (m). With respect to
its equivalence with (8a), the relation (36a) has been also
ignored. The equivalent continuity equation (36b), proposed
by L. Lorentz, is still accepted at least conditionally.</p>
<div class="art-img" id="e036">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e036.gif" class="img-responsive center-block"/></div>
<p class="art-para">
Unlike the elementary magnetic field (13b) related to a
moving charge, it is generally defined by the kinetic potential
(37a), implying the trivial equation (30).The transverse kinetic
force affecting moving electricity (37b) reminds of the curve
path of a spinning ball at the fluidic flow.</p>
<div class="art-img" id="e037">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e037.gif" class="img-responsive center-block"/></div>
<p class="art-para">
Figure 4 presents mutual relations of the static and kinetic
quantities. The equipotent static spheres, cut by the transverse

planes (Fig. 2), trace the magnetic field lines, as the isohypses
(37a) of the kinetic potential (36a). Closed into themselves,
they exclude the free magnetic poles, on the terminals.</p>
<div class="art-img" id="f004">
<img src="<?php echo $imgpath;?>images/ijpsr-116-f004.gif" class="img-responsive center-block"/></div>
<p class="art-para">

Inversely to (35b) & (37a), the convenient integrations of
the two central fields (13) give respective two potentials (38).
These two particular cases also obey the general mutual
relations (36). Unlike the two central fields (13), the first radius
degree &#8211; in these nominators, point to the energies
cylindrically distributed around the temporal or a spatial axis.</p>
<div class="art-img" id="e038">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e038.gif" class="img-responsive center-block"/></div>
<p class="art-para">
According to Einstein&#8217;s and Maxwell&#8217;s relations (11), the
force action law (39) just implies respective dynamic induction
(40). Kinetic potential is proportional with linear momentum
density. Its temporal derivative may be treated as the dynamic
potential. And finally, curl applied to (40) gives the dynamic
equation (27), as the equivalent consequence.</p>
<div class="art-img" id="e039">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e039.gif" class="img-responsive center-block"/></div>
<div class="art-img" id="e040">
<img src="<?php echo $imgpath;?>images/ijpsr-116-e040.gif" class="img-responsive center-block"/></div>
<p class="art-para">
The three EM interactions &#8211; static (35b), kinetic (37b) and
dynamic (40) ones &#8211; thus essentially represent respective
fluid-mechanical forces, at the vacuum medium.</p>
<p class="art-subhead">
Discussion</p>
<p class="art-para">
Ctg-function (17) gives the infinite field speed, approaching
the zero polar angle. According to the modern views at least,
there is no greater speeds than that of light.</p>
<p class="art-para">
As the ratio of the two transverse projections on the
sphere, this function effectively grows from the naught up to
infinity. Alike the rotational sum of resting components, this
apparent motion also implies the dynamic effect.</p>
<p class="art-para">
Apart from relativity principle, Einstein&#8217;s equation is also
here applied. On the other hand, the vector variance, from the
same theory of relativity, is renounced.</p>
<p class="art-para">
EM theory preceded the relativity. These two theories
form a causal loop, alike the two EM fields. Therefore, they
legitimately supplement and/or correct each other.</p>
<p class="art-para">
By gradual affirmation of the vacuum medium, the
material basis of physics is here called in question, including
the particles, as the carriers of the material features.</p>
<p class="art-para">
Classical physics relies on mass and electricity, as the
mere concepts, ascribed to material particles. However, the
ascriptions do not explain the concept essences.</p>
<p class="art-para">
Resolving certain forgotten problems, the new ones are
here opened, undermining the established views.</p>
<p class="art-para">
Only the clear problems can be resolved. The
reexamination confirms good, but changes bad views.</p>
<p class="art-para">
Despite the numerous expositions of EM theory, only your
own references are here mentioned.</p>
<p class="art-para">
This article substitutes the standard expositions. Even if
these latter noticed some problems, they did not resolve
them, thus not deserving the role of references.</p>
<p class="art-subhead">
Conclusions</p>
<p class="art-para">
Starting by the algebraic relations, as the simplest basic set,
the three remaining sets are completed: central laws, differential
equations and tensor forms. Thus mutually equivalent, these
four sets supplement each other in application.</p>
<p class="art-para">
The relativity principle applied to the mutual (object-field)
motion generalizes Ampere&#8217;s law to a moving dipole,
irrespective of its angular position. The restriction to the
transverse plane or to line conductors is thus transcended.</p>
<p class="art-para">
The wider sense of the algebraic from differential sets is
here resolved by the reduction to the uniform field motion, in
the both sets. This is argued by the field inertia, otherwise
being ascribed to the assumed material carriers.</p>
<p class="art-para">
A particle is manifest and interacts by its field. There is no
any proof of existence of a hard particle body, distinct from
this field. In the final instance, a particle is the center at least,
something as a knot of the surrounding field.</p>
<p class="art-para">
The force transfer is here also exceeded. Instead of the
direct action at a distance, or the successive transfer through
space, the algebraic relations describe the local field actions,
at each spatial point and temporal instant separately.</p>
<p class="art-para">
Starting by electricity of a vague essence, EM theory
seemed to be an open scientific system. The algebraic and
differential causal loops close this system. The static feedback is formally producing the apparent electricity.</p>
<p class="art-subhead" id="references">
References</p>
<ol>
<li class="ref"><div id="1">Mi&#353;kovi&#263; B. <a href="https://www.perlego.com/book/3417528/neoclassical-physics-pdf" target="_blank">Neoclassical Physics</a>. LAP LAMBERT Academic Publishing. 2019.&nbsp;&nbsp;&nbsp;<a href="#ref1"><i class="fa fa-level-up" aria-hidden="true"></i></a></div></li>
<li class="ref"><div id="2">
Mi&#353;kovi&#263; B. Essential Overview of EM Theory. Springer. 2013.&nbsp;&nbsp;&nbsp;<a href="#ref2"><i class="fa fa-level-up" aria-hidden="true"></i></a></div></li>
<li class="ref"><div id="3">
Mi&#353;kovi&#263; B. <a href="https://otik.zcu.cz/bitstream/11025/11458/1/Miskovic_1.pdf" target="_blank">Inductive Elaboration of EM Theory</a>.&nbsp;&nbsp;&nbsp;<a href="#ref3"><i class="fa fa-level-up" aria-hidden="true"></i></a></div></li>
<li class="ref"><div id="4">
Mi&#353;kovi&#263; B. <a href="https://core.ac.uk/download/pdf/295559098.pdf" target="_blank">Deductive Exposition of EM Theory</a>.&nbsp;&nbsp;&nbsp;<a href="#ref4"><i class="fa fa-level-up" aria-hidden="true"></i></a></div></li>
<li class="ref"><div id="5">
Miskovic BV. <a href="https://madridge.org/journal-of-cosmology-astronomy-and-astrophysics/ijcaa-1000143.pdf" target="_blank">Curvilinear Cosmology</a>. Int J Cosmol Astron Astrophys. 2023; 5(2): 231-236. doi: 10.18689/ijcaa-1000143&nbsp;&nbsp;&nbsp;<a href="#ref5"><i class="fa fa-level-up" aria-hidden="true"></i></a></div></li>
</ol>
</div>
</div>
</div>
</section>
</div>
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