342
PONDEROMOTIVE FORCES
we
obtain for
the
X-component
of the force
imparted
by
the
magnetic
field
strength
^x
d^x d^x
d^x
Qx
TF
+
Qy
~JJ
+
az
TF
(7)
It should
be
noted that the derivation
of
the
expressions
(6) and (7)
does
not
require
any
assumptions about the
relation
connecting
the field
strengths
(£
and
io
with the polarization
vectors and
Q.
In
the
case
of anisotropic bodies,
the electric
and
magnetic
field
strengths, respectively,
do not impart only
a
force, but also force
couples
that
act
on
the
matter. The torque
sought can
easily
be
obtained for the
individual dipoles
and summation
over
all electric
and
magnetic
dipoles
in
the
unit
volume.
One
obtains
(8)
£
=
im]
+
[OSi]}
.
Formula
(6)
yields those
ponderomotive
forces that
play
a
role in electro-
static
problems.
We
want
to
transform this
equation, applied
in the
case
of
isotropic bodies,
in
such
a
way
that it allows
a
comparison
with the
expres-
sion for
ponderomotive
forces
used
in
electrostatics. If
we
put
qj
=
(e
-
1
)*
,
equation
(6)
becomes
=
%
Oiv
®
-1
«2
rx
-
W2
•
X
The
first
two terms
of
this
expression
are
identical
with
those familiar
from
electrostatics.
As
one can
see,
the
third
term
is derivable
from
a
potential.
If the forces involved
act
upon a body
in
the
vacuum,
this
term does
not
con-
tribute
anything
on
integration
over
the
body. However,
if
the
ponderomotive
forces
involved
act
on
liquids,
then
the
part
of the
force
corresponding
to
the
third
term
is
compensated
by a
pressure
distribution
in the liquid
when
in
equilibrium.