12
DOC.
1
MANUSCRIPT ON SPECIAL RELATIVITY
equation
curl
Jj
=
-
(e +
p
+ t)
curl
e
=
c
1
+ m)
(Ia)
div
b
=
-
div
p +
p
div
h
=
-div
m
or,
if
we
introduce the
vector b
of electric
displacement
as
well
as
the
vector
of
magnetic
induction that
is
defined
by
the
equation
b
=
h + m,
even more simply,
i
curl
\) =
-
(b
+ t)
curl e
=
c
div
b
=
p
div
6
=
0
(Ia')
To these
equations
there
are
still
to
be added the
equations
that show the
manner
in
which
the
vectors
d,
b and
i
depend
on
the field
strengths
e
and
h.
In the
simplest
case,
we
have for
isotropic
bodies:
b
=
se
6
=
\ib
i
=
kt.
(8)
[p. 9] or
*
=
(e
-
1)
e
m
= (H
i
=
Ae
D*
(8')
where
e
(the
dielectric
constant), u (permeability),
and
A (conductivity) are
characteristic
constants
of the material.
Energy principle.
If
one multiplies
the first of
equations
(Ia')
by
ce
and the third
by
ch,
and adds the
two,
one
obtains,
if
one assumes
the
validity
of
equations (8),
d
itb
+
ffb
ei
=
-div
s
-
dt
...(9)
if
one again
sets
s
=
c[e,
h)].
If
one integrates
over a
finite
volume,
one
obtains,
as
in
§2,
a
dtjjCi+Jb
J
=
_
feidT
This
equation
expresses
the
energy principle
for the
case
considered here. One
sees
that the
vector
of the
energy
flux
depends only
on
the
field
strengths, exactly
as
in
the
case
where there
are no
polarizable bodies,
and that
one
has to view
eb/2
as
the