252
DOC.
11
LECTURE ON ELECTRICITY & MAGNETISM
Experience
shows
that
F1a
:
F2a
:
F3a..
=
F1b
:
F2b
:
F3b..
Thus,
the
effects
of
the
bodies
1
2
3
.. another
body
always
stand
in
the
same
ratio
no
matter how
that other
body
has
been chosen. Hence
we can
characterize the electrical
influence
of
one
el.
body by
means
of
a
number,
if
we
have
assigned an
arbitrarily
chosen
number,
for
example
the
number
1,
to the influence of
one
of the
bodies.[2]
This
number
is
called
the
quantity
of
electricity.
It
follows
from
this
definition that the
force
f
exerted
by
two
bodies
on
each
other
is
directly
proportional to
their
quantities
of
electricity.
F
=
k•e1e2.
However,
k also
depends
on
the
distance.
Further,
it follows
from
experiments
that
this
force
is
inversely
proportional
to
the
square
of the
distance, so
that
we have,
with
another
interpretation
of the
constant
k,
F
=
k6
r2
,
where k
no longer depends on
the
distance
but
only
on our
choice
of the
body
in
our
[p. 3]
group
to which
we
have
assigned
the
quantity
of
electricity 1.
The
sign
of
k
is
determined
by
our
earlier
stipulation
in
conjunction
with
experience.
That
is
to
say,
it has
been found that
quantities
of
electricity
that
are
alike
according
to
the
above
definition
repel
each other.
Thus,
k is
a positive
constant.
Its
value
depends
on
what
we
stipulate
as
the
unit of the
quantity
of
electricity. However,
we
may
also
freely
choose
k
and
thereby
define
the unit of the
quantity
of
electricity.
We
do
that
by
setting
k
=
1.
We
have
then
ex.
F


r2
In order
to
measure a
quantity
of
electricity absolutely
after
according
to this
kind of
definition,[3]
one
has to
measure,
in
principle,
a
force and
a length,
which
quantities
occur
in
the form
e
=
\/force
•
length
=
M1/2L3/2T1
This
is
the "dimension" of the
electrostatically
measured
quantity
of
electricity.
We
must
mention
a
few
more
facts
that
are
of fundamental
importance
for
the
foundations of the
theory.
If
a quantity
of
electricity
ea
is
subjected
to
the
action
of
two
quantities
of
electricity
[p. 4] e1
&
e2,
one
finds
the force
acting on
ea
from the
law
of the
parallelogram
of
forces.
In
the
special
case
where
e1
&
e2
are
very
close to
each
other,
their
effects
on
ea
will
add
up