DOC.
45 243
f
v2
_____ _____
= fi d~di~d~ +
51/2
fi
4
dedi,d~
If
one assumes
further that
no
forces
act
on
the
body
at
the
start
(t
=
t0),
then the
second of
these
integrals
vanishes.
Taking
into
account
that
II
p'
-57- d£dr]d(
is
the
E-component
KE
of
the
ponderomotive
force
acting
on
the
space
element,
one
gets
2
Lw -
4i
(
~(~K )
-~
-eli)
where
the
summation
is
to be
extended
over
all
mass
elements of the
body.
We
thus
get
the
following
strange result. If
a
rigid
body on
which
originally
no
forces
are
acting
is
subjected
to
the influence of forces that
do
not
impart
acceleration
to
the
body,
then these
forces-observed
from
a
coordinate
system
that is
moving
relative
to
the
body-perform
an
amount
of
work
AE on
the
body
that
depends
only
on
the final distribution of forces
and
the translation
velocity.
In
accordance with the
energy
principle,
from
this it follows
immediately
that the kinetic
energy
of
a
rigid
body
subjected
to
forces is
larger
by AE
than the kinetic
energy
of
the
same
body
moving
at
the
same
velocity
but
not
subjected to
any
forces.
s2.
On
the
inertia
of
an
electrically
charged
rigid
body
We
again
consider
a
rigid, rigidly electrified
body
in
uniform
transla-
tion (velocity
v)
in
the direction of the
increasing x-coordinate
of
a
"stationary" coordinate
system.
An
external
electromagnetic
field
of force
shall
not
be present.
This
time,
however,
we
shall take into
account
the
electromagnetic
field
produced
by
the electric
masses
of the
body.
First,
we
calculate
the
electromagnetic
energy