On Jul 5, 9:07*am, Cecil Moore wrote:
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 you now are in agreement that flows must balance if charge (or
energy)
is to be conserved. Excellent.

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.

For greater certainty, I paraphrase: "Only the leading edge has an EM
wave".

What is follows just after the leading edge since it is not an EM
wave?
What is it? What do you call it?


Now back to the square wave with a two year period...

After the rising edge goes by, which I assume you will still call an
EM wave, what follows until the falling edge occurs a year later?
Is it an EM wave?

If so, how is it different than what follows the rising edge of the
step wave? They both look like DC for a year.

If not, why is it not an EM wave?

....Keith

On Jul 5, 7:41*pm, Keith Dysart wrote:
So you now are in agreement that flows must balance if charge (or
energy) is to be conserved.

No, you remain confused and mistaken. Energy flows (de/dt) do NOT have
to balance. That's what I have been saying all along. Energy must
balance whether it is flowing and/or not flowing. I told you weeks ago
that the sum of your instantaneous energy flows do NOT include all the
energy, i.e. there is no such thing as conservation of instantaneous
power (energy flow). If you don't correct that basic misconception,
you will never get it.

The continuity equation aids my side of the argument, not yours. It
proves that you have been wrong all along when you did not include all
the energy in your instantaneous power equation.

Back to the LC oscillator. At the instant when all of the energy is
stored in the capacitor, energy flow has been completely destroyed,
i.e. de/dt=0, yet there is plenty of energy in the capacitor. Your
P(t)=V(t)*I(t) =0 equation completely ignores the energy in the
capacitor when I(t)=0 and I have told you all this many times before.
The continuity equation only highlights your error of ignoring the
stored energy.

After the rising edge goes by, which I assume you will still call an
EM wave, what follows until the falling edge occurs a year later?
Is it an EM wave?

If electrons (carriers) are not being accelerated and/or decelerated,
i.e. if DC steady-state exists, then there are no EM waves.
--
73, Cecil, w5dxp.com

"Cecil Moore" wrote
...

If electrons (carriers) are not being accelerated and/or decelerated,
i.e. if DC steady-state exists, then there are no EM waves.

You do not read my posts.

In the free electron laser the DC steady-state exists and there are electric
waves.
"If the electron beam is periodically deflected the current is DC but the
all
works like the dipole."
S*

On Jul 6, 2:02*am, "Szczepan Bialek" wrote:
"If the electron beam is periodically deflected the current is DC but the
all works like the dipole."

I'm afraid "periodically deflected" violates the definition of steady-
state.
--
73, Cecil, w5dxp.com

"Cecil Moore" wrote
...
On Jul 6, 2:02 am, "Szczepan Bialek" wrote:
"If the electron beam is periodically deflected the current is DC but the
all works like the dipole."

I'm afraid "periodically deflected" violates the definition of steady-
state.

In AC coulombs/s in one direction is not const In the DC is.
In this sense in the free electronn laser is DC.
S*