344
PONDEROMOTIVE FORCES
Experience shows
that this force is
independent
of
the
magnetic
perme-
ability of the material of the
conductor, and from
this it
has been concluded
that it is not
the field
strength
f),
but the
magnetic
induction Bi, that is
relevant for the
ponderomotive
force, because in the
interior
of
the
strip
the
magnetic
induction
Bi
is
equal
to
the force
ha
acting
outside the
strip
independent
of the value
of
the
strip's
permeability, while
for
a
given
external field the force in the interior
of
the strip
depends
on
u. However,
this
argument
is
not
conclusive,
because the
ponderomotive
force considered
is
not
the
only
one
acting
on our
material strip, since
the external field
ha
induces
magnetic
layers of
density1
ha
(1
-
1/u)
on
the
top
and
bottom
sides
of the
material
strip,
the layer
being negative
on
the
top,
and
positive
on
the
bottom. Each
of these layers
is
acted
on by a
force
which
is
produced
by
the
current
flowing through
the
strip;
this
magnetic
force
has
a
strength
of
i/2b per
unit
length
of the strip2
and
its direction
on
the
top
differs
from
that
on
the
bottom. The
ponderomotive
forces
so
obtained
add
up,
so
that
we
get
the
ponderomotive
force
(1
-
1/u)
i.
It
seems
that this force
has
not
been
taken into consideration
up
to
now.
The
total force exerted
per
unit
length
of
our
strip is, then,
equal to
the
sum
of the
force just calculated
and
the force
R
exerted
by
the
magnetic
field
on
the
strip's
volume
elements
due
to
the
current
flow. Since
experience shows
that the total
ponderomotive
force
acting
on
the unit
length
is
iSa
,
we
have
the
equation
or
(1
-
i)i£a
+ R
=
iSj
/r
a
\S)
R
=
1r
=
•
This
shows
that for the calculation
of
the
ponderomotive
force
R,
which
is
acting
on
the current-traversed
volume
elements,
it is the field
strength
Si
and
not
the induction
Bi
that is
responsible.
1Since
the
density
is
,
Q.
=
Bi
-
S).
=
fi
(1
-
-)
. i i
%
fl
/r
2Strictly
speaking,
based
on
the results
of
the
previous
section,
we
should
have
introduced
volume
forces instead
of
the
above
forces
acting
on
the
surface
layers,
but this
is of
no
consequence.