On Wed, 14 Mar 2007 09:09:27 -0800, Tom Donaly
wrote:
Different texts have Maxwell's equations in different order. What text
did you get this from? Becker has it (in Gaussian CGS units) as
div D = 4\pi\rho (where the backslash indicates multiplication, and D
and rho have the usual meanings. You can add the 't' if you want to, but
it's unnecessary. Also, since you're dealing in 3 dimensions, why not
indicate them as in E(x,y,z), or E(x,y,z,t) (if the time means something
to you)?

I tend to write equations in LaTeX form as most people I exchange
emails with mathematical equations use that for formatting mathematics.
Here, \pi represents the greek letter pi, and \rho is the greek letter
rho. I used x to represent a spatial 3-vector. I could have written
it as (x,y,z) but I did not think this shorthand would cause any
confusion given the context.

The difference between E and D is not important here. If you use D,
then \rho must be interpreted as the so-called "free" charge density.
However, the fundamental field is E, and if you use it the \rho must
be interpreted as the _full_ charge density. The relationship between
E and D can be very complex and may well depend upon the strength of
the applied field E. For simple materials a linear relationship is
usually assumed, e.g., D = \epsilon E, where \epsilon is the
dielectric constant of the medium. Also even here in this linear
relationship, \epsilon need not be a scalar (a number). It could be a
tensor (a 3x3 matrix), in which case D and E would not have the same
direction.

--John