6 DOC.
1
MANUSCRIPT ON SPECIAL
RELATIVITY
If
one
performs
the "div"
operation
on
both
sides,
one
obtains
I-(div
*)
=
0.
dt
Thus,
if div
h
were
at all
different from
zero,
it would have
to
be
temporally
constant.
Since this is
out
of
the
question
from
a physical
standpoint,
one
has
to set
div
ff =
0.
...(4)
Thus, to
sum up,
we
have the
following.
If
one
confines oneself
to
electrically
and
magnetically nonpolarizable
bodies and
if
one
assumes
with
H. A.
Lorentz that
there do
not
exist electrical
currents
of
any
kind other than convection
currents,
then
the
electromagnetic equations
read
curl
=
-(e
+
jp)
curl
e
=
-
-
Jj
c c
(1)
div
e
=
p
div
t)
=
0
[p. 4] §2. Energy
and
Momentum
in
Lorentz's
Electrodynamics
in
the Absence
of
Electrically
and
Magnetically
Polarizable Bodies
The
energy principle.
If
one
takes the scalar
product
of the first of
equations
(I) by
ce
and the third of
equations
(I) by
-cJ),
and
sums,
one
obtains,
using
the rule of
calculation
( )[11]
after
simple
transformation,
the
equation[12]
2 2
--div
c
[t,\f\
= 3
+ p^e
...(5)
d
2
or,
if
one
integrates
over an
arbitrary
volume while
applying (
)
f{f
\(c2
+
^2)dr]
=
/c[e®»
da~
fpnerfT'
if
one
denotes the
component along
the inside normal of the
boundary
surface
of the
space
under consideration
by
[e,
h]n.
One
may
conceive of this
equation
as
the
equation
for the
energy
balance
of
the
electromagnetic
field. In that
case w
=
1/2(e2
+
h2)
is
to
be conceived
as
the
density
of the
electromagnetic energy
and
s
=
c[e,
h]
as
the
vector
of the
energy
flow,
while
pne signifies
the
energy
taken from the
electromagnetic
field
per
unit
volume and time.
The
momentum
conservation
law.
If
one
takes the
vector
product
of the first of
equations
(I) by h
and the third
by
-
e,
and then
sums,
one
obtains first