DOC.
51
335
constant
velocity
v
away
from
the observer toward
the
plane
of
the
paper
between
the condenser
plates
A1
and
A2.
The
dimension
of the strip
S
perpendicular to
the
plates
A
shall
be
infinitesimally small
compared
to
its
dimension
parallel
to
the
plates
and
to
the dimensions
of
the plates
A;
also,
the
gap
between
S
and
the plates
A
(henceforth
called
gap
in brief) shall
be
negligible
compared
to
the thickness
of
S.
We
refer the
system
of
body
under consideration
to
a
coordinate
system
that is
at rest
relative
to
the
plates
A
and
whose
positive X-direction shall coincide
with
the
direction
of motion,
while its
Y-
and Z-axes, respectively,
are
parallel
and
perpen-
dicular
to
the plates
A.
We
will
examine
the
electromagnetic
behavior
of
the
piece
of
the
strip located
between
the
plates
A
if the
electromagnetic state
is stationary.
We
imagine
a
closed surface that
just encloses the effective
part
of
the
condenser plates
together with
that of the
piece of
the
strip
lying
between
them.
Since
no moving
true charges
nor
electric conduction
currents
exist
within this surface, the
equations
(cf.
equations
(1a) to
(4a))
curl f
=
0
,
curl
£
=
0
,
apply. Thus,
within this
space
the electric
as
well
as
the
magnetic
force
is
derivable from
a
potential.
Hence
we
immediately know
the distribution
of
the
vectors
(£
and
S)
if the
distribution of
the free electric
and
magnetic
density,
respectively, is
known.
We
shall limit ourselves
to consideration of
the
case
in which
the
magnetic
force
Sj
is
parallel
to
the F-axis,
and
the
electric force
E
is
parallel
to
the Z-axis.
We
are
justified
in
doing
this,
as
well
as
in
assuming
that the pertinent fields both within the
strip
and
within the
gap
are
homogeneous,
due to
the conditions
stipulated
earlier
regarding
the orders of
magnitudes
of
the
dimensions of
the
system
under
consideration.
We
also conclude
immediately
that the
magnetic masses
at
the
ends
of the strip
cross
section
make only
a
vanishingly
small contribution
to
the
magnetic
field.1
Equations
(13)
then
yield
the
following
relations for
the interior
of the strip:
1This
is also evident
from
the fact
that,
without essential
change
of
the
conditions,
we
could
give
the
condenser
plates and
the strip
a
circular
cylindric
shape,
in
which
case,
for
reasons
of
symmetry,
free
magnetic
masses
could
not
arise
at
all.