And now one for the engineers!

How do you interpret a non-zero Poynting vector determined by static E-
and H- fields?

What the Poynting vector actually tells us is that the flux into any closed
volume is equal to the rate of storage of energy within the volume. Since a
static field has no flux into any closed volume the poynting vector tells us
that no storage or dissipation of energy is taking place, ie it tells us
nothing and is therefore of no use in this situation.

In non-static fields it does mean something, but even here it may not
completely describe the energy flow. The Poynting Vector is just one of an
infinite number of way of describing energy flow. It is a convenient and
mathematically simple one, but not a complete solution. For instance an
alternative one is the Slepian Vector which is mathematically more
cumbersome but does include the static case.

73
Jeff