7.2 spherical coordinates
Spherical coordinates are defined
as
as indicated schematically in Fig.
7.3
.
Using the chain rule we find
once again we can write
in terms of these coordinates.
where the unit vectors
are an orthonormal set. We say that spherical
coordinates are
orthogonal.
We can use this to evaluate
,
|
(7.18) |
Finally, for integration over these variables
we need to know the volume of the small cuboid contained
between
and
,
and
and
and
. The length of the sides due to each of these changes
is
,
and
, respectively. We thus conclude that
|
(7.19) |