DOC.
52
345
To
eliminate all doubt,
we
will discuss
one more
example
which
shows
that the
principle
of
equality of
action and
reaction
requires
the
Ansatz
we
have
chosen.
We
envision
a
cylindric
conductor surrounded
by empty
space
and
traversed
by
the current
s,
which
stretches
to
infinity
along
the X-axis
of
a
coordinate
system
in both directions.
The
material
constants
of
the
conductor,
as
well
as
the field
vectors
considered in the
following,
shall
be
independent
of
x,
but shall be
functions
of
y
and
z.
The
conductor shall
be
a
magnetically
hard
body
and
shall
have
a
magnetization
perpendicular to
the
X-axis.
We
assume
that
no
external field
acts
on
the conductor,
and
thus
the
magnetic
force
fj
vanishes far
from
the conductor.
It is clear that
no
ponderomotive
force
acts
on
the conductor
as a
whole,
because
no
reaction
opposing
such
an
action
can
be
specified.
We
now
want to show
that
the
above
force indeed vanishes
given
the
Ansatz
we
have
chosen.
In
accordance with
equations (7) and
(9), the entire force
acting
on
the
unit
length
of
our
conductor in
the
direction
of
the Z-axis
can
be
presented
in the
form
(10)
R
=
0
dzZ
y
TPy
+
0
df)-
z
If
df
+
-
5
dfJ
c x
y
where df denotes
a
surface
element
of the
YZ-plane.
We
assume
that all
pertinent quantities
are
continuous
on
the
surface
of
the conductor. First
we
consider the first
integral
of
equation (10).
We
have
0
9$
y
~3y
+
0
d$)
7h
h
+
~W~
S)
IT
If
one
substitutes the
right-hand
side
of
this
equation
in
our
integral, then
the first
two
terms
vanish
on
integration
over
the
YZ-plane
because the
forces
vanish
at
infinity.
Taking
into consideration that
div
®
=
0
,
the third
term
can
be
transformed
so
that
our
integral
assumes
the
form