10
DOC.
1
MANUSCRIPT ON SPECIAL RELATIVITY
Dielectric
displacement
Dielectric
constant.
By
"dielectric
displacement"
b
we
understand the
sum
vector
sum
of the
electrical
field
strength
e
and the
polarization
p. Thus,
we
set
d
=
e +
p.
According
to
experience,
in
many
cases one
should
set d
=
Ee
for
isotropic
dielectrics
at
rest,
where
E
denotes
a
constant
characteristic
of
the
dielectric,
the "dielectric
constant." From the
equations
that define
b
and
E
we
obtain
P
=
(E
-l)e,
which
equation
likewise claims
validity only
for dielectrics
at rest.
Physical justification
of
Lorentz's
conception
of
the
nature of
the dielectric.
A
homogeneous body consisting
of
a
dielectric,
nonconductive substance
that
becomes
electrically polarized possesses
on
its
surface,
according
to
the
above,
a
layer
of
(bound)
electricity
(pn
per
surface
unit),
while the entire
density
of
(bound) electricity
vanishes
on
the inside of the
body.
If the
body
is
set into
motion,
then the electrical
quantities
on
the
surface
are
set
into motion
as
well.
Thus,
according
to
the first of
equations
(I),
they
must
produce
a
magnetic
field
and,
if
no change
in the
state
of
polarization
of
the
particles
of the
body
takes
place during
the
motion,
the
magnetic
field
so
excited will be the
only cause
of
the excitation
of
the
magnetic
field. The
existence of this
magnetic
field has been
proved by Röntgen
and
Eichenwald.[21]
Furthermore,
we
have
seen
in
§2
that
moving
electrical
quantities
in
an
electromag-
netic field
are
acted
upon by
forces that
are
given by
the
expression
e
+
-,ff]-referred to
a
unit
quantity
of
electricity.
If
the
dielectrica
really
owe
their
electrifiability
to
bound
quantities
of
electricity,
then that force
must act
on
the latter
as
well; hence,
if the
arrangement
is such that
no
electrical field
is
present,
then the
bound electrical
masses
of
a
dielectric
moving
in
a magnetic
field
must
be acted
upon
by
forces in
exactly
the
same
way
as
if the dielectric
were
at rest
and
an
electrical
field
strength
of
the
magnitude
c
acted
upon
it.
A
polarization
of
the
magnitude
p
= (e
-
1)
c
will therefore
occur
in
the dielectric. The existence of
such
a
polarization
has
been
proved by
Wilson.[22]
Electromagnetic equations
for
bodies
at
rest.
We
start
with the second
of
equations
(I).
If
we
denote the individual densities of the "bound"
electricity by
pg
and the
single density
of
the conduction
electricity by
pl,
then,
in accordance with the
explanations given
at
the
beginning
of this
§, we
must
set
div e
=
£
pg
+
£
pl.
But from the definition
given
for
p
there follows
immediately