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IN A SIMPLE CIRCUIT,
WHERE DOES THE ENERGY FLOW?
A Collection of Diagrams
12/2000 William Beaty BSEE

Electronics students commonly assume that electrical energy flows inside metal wires. Physics students know differently! Electrical energy normally doesn't flow inside of metals. In fact, the joules being sent out by batteries and generators are located in empty space: they take the form of electromagnetic fields surrounding the wires. The diagrams below will show us the details.
While a coil can store energy in the magnetic field outside its windings, and while a capacitor can store energy as an electric field in the insulating layer between the metal plates, an electric circuit handles energy a bit differently. As a whole, an electric circuit does both at once: it's both a coil and a capacitor. It's a capacitor because an e-field exists between the two halves of a simple circuit at different potentials. And it's a coil because a magnetic field surrounds each current-bearing wire. The shape of these fields will demonstrate that the EM energy which flows across a circuit is not stuck to individual electrons, nor is it moving along with the slow electrons within the interior of the metal wires. Instead the EM energy flows rapidly through the space surrounding the metal parts of the circuit.

For example, whenever a battery powers a light bulb, the battery spews electrical energy into space. That EM field energy is then grabbed firmly by the wires and guided by them. The field energy flows parallel to the wires, and eventually it dives into the lightbulb filament. There it drives the metal's population of movable charges forward, against the resisting force of electrical "friction." Electrons in the metal momentarily speed up before colliding with tungsten atoms. In this way the electrical energy gets converted into thermal energy. As a whole, an electric circuit is like a duct for electrical energy, but this duct has no walls.

[Black conductor ring with a battery inserted in one spot, a resistor inserted in another spot]
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.



[Same black ring w/battery and resistor, but with arrows depicting the circular charge-flow inside the ring.]
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.




[Same black ring with arrows, but this time with bullseyes of magnetic field distributed around the ring (the ring passes through the center of each bullseye pattern]
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".)



[Oblique 3-dimensional view of figure 3]
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.



[Battery and resistor removed from the black ring, leaving two gaps. One remaining piece of the ring has plus signs all over it. The other piece has minus signs]
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.



[The two ring-pieces above are now connected with e-field flux lines, as if the two pieces were oppositely-charged capacitor plates]
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.



[The two ring-pieces above are now connected with e-field flux lines, as if the two pieces were oppositely-charged capacitor plates]
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.



[Two earlier figures combined: the bullseyes of magnetic field and the e-field flux lines are drawn surrounding the black conductor ring.]
Fig. 6 E-FIELD AND B-FIELD TOGETHER



[3D oblique version of fig 6]
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.



[A new field surrounds the black ring. The field lines spew out of the battery, flow in the space around the ring and parallel to the two halves of the ring, then dive into the resistor.]
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.)



[The energy-flow field as in the previous diagram, but with the flux-lines of e-field lightly sketched in]
Fig. 8 ENERGY FLOW FIELD WITH E-FIELD IN GRAY
Note that the energy always flows perpendicular to the lines of e-field



[Again the energy-flow field, but with the bullseyes of magnetic field lightly sketched in]
Fig. 9 ENERGY FLOW WITH B-FIELD IN GRAY
Note that the energy always flows perpendicular to the lines of b-field too.



[The black ring conductor with ALL the flow lines and field lines. It looks like an obscure mess.]
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.

SEE ALSO:

Poynting-flow diagrams are extremely rare in physics texts, and the majority of physics instructors seem unaware that they exist. Perhaps the reason is, that while still children, we were all taught that energy flows inside the wires. These childhood science misconceptions are extremely difficult to change. Our physics misconceptions frequently remain unexamined, and often persist well into adulthood science and engineering careers. For example, RP Feynman mentions the Poynting-flow concept in "The Feynman Lectures," Chapter 27, and performs EM-field energy flow analysis on capacitors and resistors. But then he doesn't analyze 2-wire transmission lines, nor does he link all the components together into a continuous system as with my figure 7 above. Worse, at one point he angrily bad-mouths the whole concept, and insists that the evidence shouldn't lead us to change our original viewpoint. Instead he suggests that we continue to assume that the energy flows inside the copper! This is Feynman?!! Counciling dishonesty rather than harnessing an "alternate toolkit?" Amazing. (And ...doesn't he know that the speed of light within solid copper, the speed which causes Skin Effect phenomena, is down in the meters per second range? How then can electrical energy cross the circuit so quickly?)

If the common misconception that "energy flows inside wires" has had such a deleterious effect on an honest free-thinker like Feynman, imagine the trouble a more conventional mind would have with it. No joke, I see this as quite a frightening issue.

Here's another version of my figure 7:

page 417, Fig 10-19, found in:
ELECTROMAGNETICS 2nd Ed., John D. Kraus & Keither R. Carver, McGraw-Hill 1973
This one above is interesting, because it shows one place where poynting vector energy flow is a crucial idea: Antenna Design! Kraus' Electromagnetics is essentially an antenna design book aimed at physics students. (But note that Kraus makes an important point: the source in the above diagrams ...is a battery! The propagating EM flow has 0Hz frequency.)

Below is another one for convenient use:
http://amasci.com/elect/poynt/poynt.html
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