On Dec 28, 8:37*am, Roy Lewallen wrote:
Keith Dysart wrote:
On Dec 28, 1:38 am, Cecil Moore wrote:
Keith Dysart wrote:
Perhaps try googling "in the limit as t approaches 0..."
So how many joules can pass a point in zero seconds?

You have descended into silliness. You are out on your
Harley doing 60 miles/hour. How far do you travel in 0
seconds?

So your point was?

But at least you now see the utility.
Nope, I don't. I don't think the concept of instantaneous
power is mentioned at all in "Optics", by Hecht.

Ahhh. The difficulty is because you don't "think" that
the concept is mentioned in Hecht. Could that be because
at 5E14 Hz, it is difficult to measure? Try a circuit
analysis or transmission line book. You will have more
luck. There is a good chance that your Ramo and Whinery
mention it. Look near where they derive
Pavg = Vrms * Irms * cos(theta)

...Keith

Ramo, Whinnery, and Van Duzer, _Fields and Waves in Communication
Electronics_: p. 16 (in derivation of Eq. 3).

Van Valkenburg, _Network Analysis_: Eq. 14-2, p. 420.

Pearson and Maler, _Introductory Circuit Analysis_: Eq. 5.42, p. 251.

Weidner & Sells, _Elementary Classical Physics, Vol. 2_: Eq. 30-10, p. 912..

_IEEE Standard Dictionary of Electrical and Electronics Terms, Third
Ed._: "Power, instantaneous (two-wire circuits)"

Roy Lewallen, W7EL

That last one will be of particular interest to Cecil.
Its in the Seventh Edition, as well, on page 562.

Of possibly even greater interest to Cecil is the
second entry following 'instantaneous power'...

"instantaneous Poynting vector (P
(t,
r)) (of an
electromagnetic wave) The vector product of the
instantaneous electric and magnetic field vectors.
The integral of P
(t,
r) over a surface is the
instantaneous electromagnetic power flow through
the surface."

...Keith