chuck wrote:
OK, I'm a little confused. Well, maybe more than a little.

Starting with energy as the "ability to do work" and power as the rate
at which energy is "transformed" into work, things quickly get muddy.

Power is the rate at which energy is transferred or used. Period.

Energy passing through an imaginary surface (or point or plane) would
not actually do any work in passing through, and in fact would retain
its full potential to do work after having passed through.

Yes.

What then is power density? Is it the amount of work that the energy
passing through a unit area of the surface "could have done" had it been
actually and fully "captured" at that surface?

No. Power is not an "amount of work", nor is power density. Power is the
rate at which power is being transferred, so it can tell you only the
rate at which work can be done, not the amount. The rate at which energy
is being passed through a given cross sectional area of a surface is the
power density. If you integrate the power going across the boundary for
some period of time, you then know the amount of energy which has
passed, and therefore the amount of work which can be done.

There is no real power at
that surface, is there?

There is real energy passing that surface, and the rate at which it's
passing is the power at that surface. So yes, there is.

While power (and work) absolutely require energy, it strikes me as
metaphysical whether all energy ultimately does do work and produce
power. I don't think physics requires that, and it seems that lot of
radiated energy is not obviously being transformed into work. So is
energy without power really impossible, Cecil?

Cecil loves metaphysical arguments, so this is an ideal question for him.

Been away from this for a longer bit than I'm comfortable mentioning.

Try finding a basic physics textbook at your local library. Most high
school level texts should cover the topic adequately. For a more
mathematical and quantitative treatment, a freshman level college text
would be fine. A couple of the more popular ones are Resnick & Halliday,
and Weidner & Sells. In the older editions of both, at least, electrical
phenomena are covered in the second volume. However, power, work, and
energy aren't restricted to electricity so are covered in general terms
in the first volume.

Roy Lewallen, W7EL