Poynting vector

The Poynting vector is the arrow that tells you which way electromagnetic energy is flowing and how much of it streams through each square metre every second. Wherever an electric field and a magnetic field cross, energy marches off in the third perpendicular direction — point your right hand's fingers from E toward B, and your thumb points where the power goes. It's measured in watts per square metre (W/m²), the same units as the sunlight warming your face: about 1,000 W/m² of Poynting flux from the noonday Sun.

The surprising lesson of the Poynting vector is that energy in a circuit doesn't actually travel *inside* the wires — it flows through the empty space *around* them, guided by the fields the wires set up. The copper is just a rail that shapes the field; the real river of power runs in the air alongside. This is why a transmission line or a coaxial cable can carry kilowatts: the energy rides the field in the space between conductors, and the metal merely steers it. The same vector explains how an antenna launches power into the sky and how a laser delivers a concentrated beam.