Right hand rule modified 20111224
When you grab a ring with your right hand, the thumb points in the toroidal direction along the ring while the fingers curl through the area of the ring in the perpendicular poloidal direction around the tube. Poloidal flux, which occurs through an area, and perpendicular toroidal looping around, which occurs along a circumference, are always associated. A flux or current has magnitude and direction. It has a rate of change d/dt, if its direction changes, even if its magnitude, area or circumference do not change.
The flux of red E and green B, seen below, are as real as a mudslide. If they are real, what are they? We know their units. The mathematical interaction of units tells us something about the consistancy of our world model but one might mistake superficial knowledge of units for the deep knowledge of reality.