The thorny way of truth - Free Energy Community

" 116 - Marinov
3-(V.grad)A, (10)
where the space and time derivatives are taken with respect to the laboratory, as we
work only within an accuracy of the first order in \//c^'^'°, and, for brevity, we
write all laboratory quantities in the last equation (and further in this paper) without
primes .
Comparing formulas (5) and (10), we see that the "potential" (i.e., right) parts of
these equations differ with the three last terms in equation (10). We see that the
electric (i.e., related to *) absolute effects are proportional to v/c and for this
reason they are small. I repeat, in Ref. 7 I proposed a method for measuring such effects.
However, the magnetic (i.e., related to A) absolute effects are not only comparable
with the relative magnetic effects but are even much bigger, because the former
are proportional to V/c, while the latter are proportional to v/c and for macroscopic
charged bodies V is always much bigger than v. Later I shall show the reasons for which
absolute magnetic effects have not been observed until now.
Conventional electromagnetism treats only the electric and magnetic intensities,
t and B (see their mathematical expressions through the potentials in the text after
the formula (5)), as real physical quantuties. For conventional electromagnetism, the
electric and magnetic potentials, and A, are "second quality" auxiliary quantities
which can be changed at will using the so-called gauge transformation^ to the degree
that the intensities calculated with the new potentials remain always the same. This
is a terrible aberration which reins in physics since a century (see also p. 124).
Indeed, the last term in formula (10) shows clearly that the V-vector-gradient of
the magnetic potential takes part in the potential force acting on the test charge,
i.e., that the magnetic potential is an observable physical quantity ". Throughout this
paper the extreme importance of the last term in formula (10) will be revealed, so that
the potentials will be again enthroned as the legitimate electromagnetic king and
queen of noble German descent and the intrusive intensities of a Saxon mean birth will
be chasen away.
Let us suppose that the magnetic intensity is uniform (constant), i.e.,
B = rotA = Const, (11)
in a certain space domain. In such a case the following mathematical relation takes
place ^ ^ ^ ^ ^ ^ ^
rot(Bxr) = -(B.grad)r + Bdivr = - ^ + 3§ = 2B, (12)
where r is the radius-vector of an arbitrary space point in this domain. Substituting
(12) into (11), the following relation can be established between a constant magnetic
intensity and its magnetic potential
^ = ^Bxr + ^Q, (13)
where A is an arbitrary vector whose rotation is equal to zero, i.e., rotA = 0. Putting
now (13) into the last term of equation (10), we obtain, if choosing A^ = 0,
^(V.grad)A - |-(V.grad) (Bxr) = ^Bx(V.grad)r =
^ BxV = - ^ VxB = ^
VBy, (14)
-*
where the result on the right side is written for the case that V is directed along
the x-axis and that B is directed along the z-axis. When B is directed along the z-axis
the first term on the right side of (13) can be presented in components as follows
(l/2)Bxr = (-yB/2, xB/2, 0). Such is the magnetic potential in a long cylindrical solenoid
whose axis is along the z-axis, and I sav that the magnetic potential has a
circular symmetry . If we choose now the vector Aq i" (13) as follows Aq = ^B/2 , xB/2 , 0)
we see that its rotation is equal to zero, and for the vector A we obtain A = (0, xB, 0),
Such is the magnetic potential in a long rectangular solenoid whose yz-sides are much
larger than its xz-sides, and I say that the magnetic potential has a rectangular sym -
metry . Putting the last magnetic potential A (i.e., this one with a rectangular sym-^
metry) into the last term of equation (10), we obtain, at the above assumption that V is
directed along the x-axis,
a(V.grad)A = ^vi-(xBy) =§VBy. (15)
and one can assume that for B = Const the last two terms in (10) cancel each other.