320
DOC.
11
LECTURE ON ELECTRICITY & MAGNETISM
4njx
+
4njz
+
dt
dy
dz
dt)y
d£x
d§2
dt
dz
dx
d%2
_
dZy
H
CO
1
d!\D
4njy
+
1-~
=
in vector not.
4nj
+
--
=
curl
§
dt
dt dx
dy
These
equations
are
joined
by a
fourth
one,
that of Gauss's theorem
4nE
da
8TX
dTv
dT)z
.
,.
4np
=
+
-r1
+
-r1
4nP
=
dlv ®_
If
one
bears
in mind
that
(div ®)
=
0.
5p
=
_
dt
dx
dJl
+
9jy
dx
dy
dy
dz
dj,
+
'»
dz
=
-div
j,
then
one
has
4n
div
j
+ d_
dt
But
this
equation is
contained
in
the
ones above,
as one
can
see
by
differentiating
with
respect
to
x,y,z
and
adding.
As
usual,
it
is
assumed that
j
and
30
are
determined
by &
.
The
simplest hypothesis
is
jx
=
°&x ©x
=
C«x
------- --------
-------
--------
However,
the relation
can
be
a more
complicated one.
[p.
72]
3)
This
was
the
law
that defined the
magnetic
fields
determined
by
electric
currents.
We
have also
become
acquainted
with
a
law
for the
production
of electromotive
effects
by
the alteration of
magnetic
fields.
dN
e
=
-
-
dt
This holds first
of
all
for
closed circuits.
If
we
think of
the
EMF
as a
line
integral
of
an
EMF
field
e,
then the
law
takes the form
$tßs =
-jJl*ßo
Because of the
finite
propagation
velocity
of electric
effects,
this
law,
too,
will
only
hold for
oo
small surface
elements. We
apply
it to
the
following
surface.