IN A SIMPLE CIRCUIT, WHERE DOES THE ENERGY FLOW?
A Collection of Diagrams
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
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
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
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
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
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.
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
remain unexamined, and often persist well into adulthood. 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
link all the components together into a continuous system as with my
figure 7 above. Worse, at one point he angrilly 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 this "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,
imagine the trouble a more conventional mind would
have with it. No joke, I see this as 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
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