DOC.
45
245
This
contradiction is resolved
by
the results of the
previous
section,
i.e., the kinetic
energy
of the
body
under consideration
cannot be
calculated
like that of
a
rigid
body
upon
which
no
forces
are
acting.
On
the
contrary,
in accordance with
§1,
we
must
take into
account
that
our
rigid
body
is
subjected
to
forces
caused
by
the interaction
between
the electric
masses.
Thus,
if
we
denote
by
K0
the kinetic
energy
in the absence of electric
charges,
we
obtain for the
body's
total kinetic
energy
K
the expression
=k0+AE+(E-E) es, -
F3)
where
Es
denotes
the electrostatic
energy
of the
body
in the
state
of
rest.
In
our
case
we
have
A*
=
-
$
ßh
tx
W
dX'
+
W
dV
+
~K~\
dZ'
d{dr]d(
,
from which
one
obtains
by
integration
by
parts, taking
into consideration that
X', Y',
Z'
can
be
derived
from
a
potential,
a
E
=
%ßh
_
y12
-
Z]2
d(drjd(
If
one
takes into
account
the
expressions
for
K0
and
ß
given
in
§1,
one
obtains the
following expression
for the kinetic
energy
of
the
electrified
rigid
body:
E
K
=
I1
+ 7I
yi
1
-
1
7
1
"
(7)
This
expression
is,
as
it
must
be,
independent of
the
body's
orientation
relative
to
the direction of translation. If
one
compares
the
expression
for
K
with that for the
energy
K0
of
a body
not
charged
electrically,
11
-1