336
EQUATIONS
FOR MOVING
BODIES
Dz
+
v/c
By
=
,
By
v/cE2
Jy
By
+
v/c
=
.
* c
y.
®
+
-
£ =
a
y
c z
^
%
*
f
*.
These equations
can
also
be
written in the
following
form:
(1)
1
-
ep
-p v*
®.
=
|(e/i
-
!)£
+//
1
1 "
^
vi
£
y
i
-
A*
H
=
e
1
"
V +
f(^
-
my
Concerning
the interpretation
of
(1)
we
remark
the
following: The
dielectric
displacement
©
experiences
no
jump
at
the surface of the strip,
Z
hence
it
equals
the
charge
of
the condenser
plates
(more
exactly, of
the
plate
A1)
per
unit
area.
Further,
(E
x
S
equals
the
potential
difference
between
Z
the condenser
plates
A1
and
A2
if
S
denotes
the separation of the plates,
because if
one
imagines
that the strip is
separated
by
an
infinitely
narrow
slit
running
parallel
to
the
XZ-plane,
then
E
equals
the electric force in
the
slit
on
account
of
the
boundary
conditions
holding
for
that
vector.
Next
we
consider the
case
that
no
magnetic
field excited
from
the
out-
side
is
present,
i.e.,
according to
the
above,
that in
the
space
considered
the
magnetic
field
strength vanishes.
Then equations
(1)
will have
the
following
form:
1
vl
1
^
*y
- !«•
" '
1
"
^
V 1
V1
1-
F
S
z
Since
we
must
have
v c,
the coefficients
of
(E
in
the
last
two
equations
Z
must
be
positive
if
t\i
-
1
0.
In
contrast,
the coefficients of E and
y
©
are
larger, equal to,
or
smaller than
zero,
respectively,
depending
on
z
whether
the velocity
of
the
strip
is
smaller,
equal to,
or
larger
than
c/eu,
i.e.,
than the velocity of the
electromagnetic
waves
in the strip
medium.
Hence,
if
(£
has
a
fixed value, i.e., if
one
applies
a
fixed
potential
Z