On Jul 4, 8:24*pm, Keith Dysart wrote:

From Wikipedia, I have just learned that the concept I am
attempting to describe is known as a "Continuity equation".

In all your previous equations, you have presented only the first term
and completely ignored the second (delta-dot-v) term of the equation
which is required for balance. When you add the proper term, i.e. you
track and account for all of the energy, your energy equation will
balance - as I told you days ago.

So how do you characterize a slow square wave? Say one that is 0V for
one year, then 10V for a year, then 0, then...

The same way I characterize, "How many angels can dance on the head of
a pin?" The length of time makes absolutely no difference to the
concept involved. The above conditions do not match the DC steady-
state conditions of your earlier example.

With an infinitely long transmission line excited by a step function,
is there an EM wave propagating down the line?

Yes, there is an EM wave at the leading edge. Electrons cannot move at
the speed of light. But it is impossible to window such an example in
a valid manner because windowing creates other EM waves where none
exist in your example. There is no trailing edge in your example yet
windowing would necessarily create a trailing edge. Since an
infinitely long transmission line is impossible, we are back to the
"angels on the head of a pin" problem. In any region of the example
where steady-state DC conditions exist, EM waves have ceased to exist.
That's what happens when you make the line a fixed length and
terminate it at that point. Anywhere DC steady-state conditions exist,
your DC forward and reflected wave analysis falls apart.
--
73, Cecil, w5dxp.com