DOC.
52
343
§2.
Forces that
depend
on
the
velocities
of
the
elementary
particles
We now
turn to
the part
of
the
ponderomotive
force that is
produced
by
the velocities
of motion
of
the
elementary charges.
We
start
from
the Biot-Savart
law.
According
to
experience,
the force
that
acts
on a
unit
volume
of
a
volume
element
traversed
by a
current and
located
in
a
magnetic
field is
i
W]
,
if the
matter
traversed
by
the
current
is
not
magnetically
polarizable.
As
far
as we
know,
for
the
interior
of
a
magnetically
polarizable
body
that force
has
so
far
been
set equal1 to
i
[«»]
,
where
denotes the
magnetic
induction.
We
will
now
show
that the force
acting
on
the
current-carrying
volume
element
is
also obtained in the
case
where
the current-traversed
matter
is
magnetically
polarizable
if the
volume
force
(9)
\
m
[8]
is
added
to
the force
expressed
by
equation
(7).
We
will first illustrate
this
by a
simple
example.
Let
the infinitely thin strip
S,
plotted
in
its
cross
section, stretch
to
infinity in both directions
perpendicular
to
the
plane
of
the
paper.
Assume
that it consists of
magnetically
polarizable
material
and
is
located in
a homogeneous
magnetic
field S),
whose
direction is
indicted
by
the
arrows
Uj
(cf.
figure).
We
ask
for the force
acting
on
the material strip if the latter
is traversed
by
a
current i.
I
F
s
+ + + + + + + + + + +
b
1Cf.,
e.g.,also
M.
Abraham,
Theorie
der Elektrizität
2
(1905):
319.
[7]