DOC.
1
MANUSCRIPT ON
SPECIAL RELATIVITY
13
density
of the
electrical
energy
and
hb/2
as
the
density
of the
magnetic
energy.
2
We
can
decompose
this
energy density
of
the
electromagnetic
field into the
following components
w,
we,
and
wm:
e2 +
w
=
-
we =
2
1 P2
=
m
e
-
1
2
1
m2
n
-
1 2.
This
decomposition
is
called for from the
physical standpoint
in the
light
of Lorentz's
theory.
For
w
is
the
purely
electromagnetic energy density
that the field
would
possess
even
in the absence of
polarizable
bodies.
we
is the
density
of the
energy
that
one
has
to
apply
so as
to
endow the medium with the
polarization
p
opposing
the
elastic forces between
the bound electricities and
matter. Thus,
this
energy
attaches
to matter
and has
nothing
to
do
directly
with the
electromagnetic
field;
it
need
not
be
viewed
as
electromagnetic energy, being,
instead,
only
connected with it
by
virtue
of the
properties
of
matter.[24]
The
same applies
to
wm.
We
can
write for
(9):
dw dvv 3vv
et
=
-div
s
- -
-- -
...
(9a)
dt dt
dt
Ponderomotive
forces
exerted
on
bodies
at rest.
We first seek these forces for the
special
case
where
only
an
electrostatic field is
present.
We
inquire
after the work A'
that the field
supplies
in the
course
of
infinitely
small
displacement
s
of the material
particle.
The
ponderomotive
forces
acting
on
matter
can
then be deduced from this
work. From the
energy principle
one
obtains
A'
=
ed/2
where
"ö"
denotes the
change
that the
quantity appearing
behind
ö
experiences
as
a
result of the
displacement.
Because
of
the third of
equations (Ia'),
e
can
be
[p.
10]
presented
in the form
-grad
p,
so
that,
because of the first
of
equations (8)
and the
second of
equations (Ia'),
the
energy
of the field
can
be
written in the form
1/2egrad2pdr
as
well
as
in the form
1/2pdr.
Thus,