onsider this example: wrap the entire circuit lo
Unfortunately, I think this your example is getting away from any point I can absorb.
More from Wikipedia:
gives an expression for the Poynting vector:
which physically means the energy transfer due to time-varying electric and magnetic fields is perpendicular to the fields
This quote specializes in the application to time-varying E and H, which I doubt is an exclusive application of the Poynting vector. If we take the equation quite literally it says if there are any non-colinear E and H fields, then there is a non-trivial Poynting vector and associated energy flux.
My conclusion is that:
Since the E and H fields are static or dynamic in a 3-dimensional space, it implies that the Poynting vector exists and is also a 3-dimensional function at whatever localized position in 3-D space that it is evaluated.
I guess it is certainly possible to misapply any theory, but I fail to see any particular application where the Ponting vector is inapplicable save for the colinear case mentioned above where the cross product does to zero.
This picture on Wikipedia is essentially the same example as the video other than a resistor is used in place of the light. Maybe the video adapted this picture and so whatever error you are seeing is not from the video but rather from
Chetvorno,
King of Hearts (the Wikipedia author)
English: A simple DC circuit consisting of a battery
(V) and a
resistor (R), showing the
Poynting vectors (S, blue arrows) in the space surrounding it, as well as the fields it is derived from, the
electric field (E, red arrows) and the
magnetic field (H, green arrows). The Poynting vector {\displaystyle \mathbf {P} =\mathbf {E} \times \mathbf {H} }
represents the direction and magnitude of the power flow in the electromagnetic field (the length of the vectors shown here are not to scale; only the direction is being shown) In the region of space around the battery, the Poynting vectors are directed outward, indicating that power flows out from the battery into the electromagnetic field. In the region of space around the resistor, the Poynting vectors are directed inward, indicating that since the resistor consumes power, the power enters it from the field. On any plane
(P) located between the battery and the resistor, it can be seen that the power flux though the plane is directed toward the resistor.