IN A SIMPLE CIRCUIT, WHERE DOES THE ENERGY FLOW?
A Collection of Diagrams
William Beaty

Fig. 1 A SIMPLE CIRCUIT A battery is connected to a resistor such as a light bulb. The battery converts its chemical fuel into waste products, and the resistor gets hot.

Fig. 2 THE CONDUCTIVE PATH: CURRENT All conductive materials contain movable charges. The resistor and the battery's electrolyte both are conductive. When we include them with the wires, we can see that an electric circuit is a complete circle which is full of "fluid" charge. It acts like a liquid flywheel; a flywheel hidden inside a closed ring of pipe.

Fig. 3 THE MAGNETIC FIELD CAUSED BY THE CURRENT LOOP A circular electric current is an electromagnet. The magnetic field-lines form rings around the conductors. Note that I've slightly tilted the circles to make them visible. In reality, we should be looking at them edge-on. (Also: note that the physics name for the magnetic field is "B-field".)

Fig. 3A THE MAGNETIC FIELD CAUSED BY THE CURRENT LOOP Here's a better view of the above circuit... the three-dimensional oblique view. To be more accurate, we need to draw more than just two patterns. Between the two patterns above, draw a third. Then between each of those draw more and more. The end result looks like "tubes" of magnetic flux surrounding the wires.

Fig. 4 TWO CHARGED CONDUCTORS: VOLTAGE Everything connected to one battery terminal acquires the same electrical potential (voltage.) The circuit acts like two separate conductors, one with a positive charge imbalance and one with negative.

Fig. 5 THE ELECTRIC FIELD CAUSED BY THE OPPOSITE CHARGES The two charged wires act like the plates of a capacitor. "Force lines" of e-field spew out of one charged conductor and dive into the other. This is a side view of the e-field in the plane of the circuit. In a full 3-D view we'd see the lines spreading outwards in radial star-shapes from each wire.

Fig. 5A THE ELECTRIC FIELD CAUSED BY THE OPPOSITE CHARGES Again, here's a 3D oblique view. The two halves of the circuit act as opposite-charged wires with e-field flux connecting them. As with figure 3A we need to draw a third pattern between the two above, then draw more between those until the whole wire is covered with bent sheets of electrostatic flux which arcs between the wires.

Fig. 6 E-FIELD AND B-FIELD TOGETHER

Fig. 6A E-FIELD AND B-FIELD TOGETHER The 3D oblique view of the two fields. Add more and more patterns between the two shown above, until empty space is packed full of "hair." Note that most of the flowing energy lies between the two wires... but quite a bit also surrounds the "cable pair" as a whole. Also note that the E and B flux lines are always at 90 degrees to each other. When we say that E and B in light waves are always perpendicular, the above diagram shows what such a thing looks like.

Fig. 7 THE ENERGY FLOW (POYNTING FIELD) Electromagnetic energy flows out of the battery and into the empty space around the circuit. It flows parallel to the connecting wires, then it dives into the resistor. The field of energy flow is found by multiplying the e-field by the b-field (E x B vector cross-product.)

Fig. 8 ENERGY FLOW FIELD WITH E-FIELD IN GRAY Note that the energy always flows perpendicular to the lines of e-field

Fig. 9 ENERGY FLOW WITH B-FIELD IN GRAY Note that the energy always flows perpendicular to the lines of b-field too.

Fig. 10 A SIMPLE CIRCUIT? When all the separate invisible phenomena are displayed together, you can see why "electricity" might be a bit hard to understand. And this diagram only shows a two-dimensional slice; a sort of side view of the fields. The real fields are 3D and volume-filling, so an accurate drawing would look like a black glob of hairs.