Steve Kanim, who is a professor and physics education researcher at New Mexico State University, brought this cool puzzle to my attention a few years ago:
If you calculate the poynting vector for a current carrying resistor–considering the E field that drives the current and the B-field generated by the current, you get that the energy flux in the resistor is directed radially inward toward the center of the wire. If you don't believe this, figure out the direction of those fields, and use the right hand rule to calculate the cross product. At first glance, this seems kind of weird. You would think that the EM energy would be directed outward, because, well because a lightbulb is a resistor, and a light bulb emits light, and that light is electromagnetic waves, and that light is certainly traveling away from the light bulb. Of course, there is nothing deeply troubling here, but that doesn't mean it isn't worth thinking through.
I'm curious: How are you making sense of this seemingly odd result? Are there different ways that you might make sense of it?