DOC. 9 FORMAL FOUNDATION OF RELATIVITY
63
Electromagnetic equations
of
moving
bodies
for
the
case
considering
only
bodies
with
dielectric
constant
1
and
magnetic permeability 1.
Let
us
consider the electric
and
magnetic polarization
of bodies
only
insofar
as
they
cause
electric and
magnetic
%
charge
densities;
there shall be
no
electric
or
magnetic "polarization
currents."
Electric conduction
currents
along
conductors, however,
shall be considered. The
general-covariant
field
equations
for this
case
are
found
by taking
into
account
(on
the
right-hand
sides of the
equations)
the electric and
magnetic
convection currents
as
well
as
the electric conduction current
along
conductors.
Let
p
be the
charge density
of
polarization
electrons and conduction electrons
combined,
as
has been
previously
defined.
p«
dx
ds
-
is then the V-four-vector of the
convection
current, produced
jointly
by polarization
electrons
and conduction
electrons.
Let
p
be the
previously
defined
magnetic charge density
that
originates
from
the
(rigid) magnetic polarization.
P(m)
dx
ds
;
is then
the
V-four-vector
of
the
magnetic
convection current.
Another V-four-vector will
correspond
to the conduction
current,
and
we
shall
denote
by
it
(8M).
It is determined
by
the fact that in the "normal
system"
"1
,
-.14
8
=
-Ag
and,
on
the other
hand,
82
=
-
^ A^
24
«3
,
^34
8
--A8
8=0
dxx
ds
=
0,
dx7
ds
=
0,
dx2
ds
=
0,
dxA
ds
=
1
{12}
These
conditions
are
met
by setting
aß
"S
The field
equations
then turn out
to
be
E
dfT.
v
dxv
P(e)
dx£
ds
+
8'
E
a?r
v
dxv
P
(M)
dx
ds
(55)
(56)
Field
equations
for
isotropic, electrically
and
magnetically polarizable moving
[p. 1065]
bodies.
We
modify
the
case
which
we
just considered,
and
now
also take into account
electric and
magnetic polarization
currents. It is assumed that
in
the co-moved normal