ARGUMENTS ABOUT ELECTRICAL ENERGY FLOW
In wires, where does the energy flow? Does it move along w/electrons?
1997 W. Beaty
FROM AN OLD EMAIL DISCUSSION
On Thu, 26 Jun 1997, xx wrote:
> All contain a lot of imprecise/misleading concepts just as you pointed
> out in you discussion of "charge".
> "ELECTRIC ENERGY IS NOT CARRIED BY INDIVIDUAL ELECTRONS"
> It most certainly is. It is the kinetic energy of the electrons. I am
> assuming you are talking about the energy in an electrical "circuit".
(Yes, energy in a circuit.)
I guess my original article is not clear enough. Here it is again:
> ELECTRIC ENERGY IS NOT CARRIED BY INDIVIDUAL ELECTRONS
> > Some books teach that, in a simple battery/bulb circuit, the
> > electrons deliver energy to the bulb, and then they come back empty
> > and need to be re-filled with energy by the battery. This is
> > wrong. Some books give an analogy with a circular train track full
> > of freight cars waiting to be filled. This is wrong. The energy in
> > electric circuits is not carried by individual electrons, it is
> > carried by the circuit as a whole.
Are you objecting only to the boldface statement above? Or do you really
believe that a battery fills each electron with energy, then each electron
rushes nearly instantly through the wire to the load, dumps its energy,
and the "empty"
electrons rush back to the battery? If you think that energy
flows along with the speed of the current, you are wrong. I
suspect that my boldface statement above might not be clear enough, and
also suspect that you may have missed the text below it which attempts to
clarify my meaning.
I intended to communicate a simple idea: individual electrons in a
circuit do not behave as "energy buckets." When electrical energy
propagates from source to load, individual electrons themselves DO
NOT move all the way from source to load. Instead, a battery injects
electromagnetic energy into one spot in a circuit and the EM energy
propagates among the population of electrons at the speed of light, while
the individual electrons themselves only drift very slowly at very low
If you really do believe the "energy bucket" explanation of energy
delivery, then let me point out something. In a commercial AC system the
generator pumps electrons back and forth. The max drift-velocity of these
electrons is in the range of cm/hour. The total back-and-forth motion of
the electrons in a 60Hz AC conductor can be calculated, and it works out
to be much less than a mm. If this is true, how can the "full" electrons
in the generator ever get to the load in order to dump their stored
energy? If the generator injects energy into electrons, how can they get
to the distant load if they wiggle back and forth?
The answer is that
the electrons do not travel to the load. Instead, they transfer
between their neighbors, and the electrical energy propagates along the
column of charges within the wire. The electrons are the "medium," and
the EM energy is wave-energy. The EM energy moves from electron to
electron (it's like any waves, such as the waves which occur when a hammer
strikes the end of a very long rod.) The EM energy does not propagate via
individual electrons, instead it flows as an electromagnetic wave through
the population of electrons. The energy-wave uses the electrons as a
propagation medium. If it did not, then the EM energy coming from the AC
generator would flow outwards into space rather than moving along the
wires in the circuit. Whenever people get confused about charge-flow
versus energy flow, it's just the old problem of waves versus their
> "ELECTRIC ENERGY IS NOT CARRIED BY INDIVIDUAL ELECTRONS" - it most
> certainly is. It is the kinetic energy of the electrons.
No, the kinetic energy of individual electrons has a vanishingly small
impact on circuitry. The mass of each electron is way too small!
Instead, the energy in an electric circuit is contained in the energy of
the electrostatic and the magnetic fields produced by the electrons. The
small drift velocity of electrons, as well as their tiny contribution to
the total mass of the wires, leads to values for kinetic energy which are
far far smaller than the energy contained in the fields, and so the
KE contribution of electrons can be ignored.
Imagine a simple battery/bulb circuit. Two wires connect the battery to
the bulb, and the blub creates light. The value of electric current is
the same in both wires, hence the electron drift velocity and the kinetic
energy of the individual electrons is the same in the outgoing wire and
the return wire. But if the entire energy was actually in the KE of
then how can any energy be delivered to the bulb? Note that the electrons
flowing in the circuit don't lose any net KE in passing through the bulb
filament, their average velocity on the return trip is the same as their
average velocity on the outwards trip. In reality the energy is contained
in current AND potential of the circuit, in amperes AND volts, and if we
wish to learn the rate of energy transport from battery to bulb, we must
know the potential difference-between the wires as well as knowing the
value of electric current. But knowing the velocity and the mass of each
electron doesn't help us one bit.
If by "kinetic energy of electrons" you refer to the energy stored in the
b-field surrounding a moving electron, then yes, the energy in a circuit
is partly contained in the "KE portion" of the EM field; in the b-field.
However, this is an incomplete description, since energy is also contained
in the electrostatic fields surrounding a circuit; it is contained in the
"voltage", in the altered potential energy of the electrons and protons.
Both b-fields and e-fields play a role. If a circuit contains only KE
(magnetism and current) and no PE (no net charge or voltage), then you
have a magnetostatic situation where the carriers move in a circle like a
superconductive energy-storage coil (like a flywheel;) and in that case
the electrons coast
freely, and there is ZERO net transport of energy from source to load.
With just KE alone, there may be lots of energy stored in the circuit as
but this energy remains in one place and does not propagate from source to
Two ways to visualize the energy flow in a circuit:
> ELECTRIC CURRENT IS NOT A FLOW OF ENERGY - The term "electric
1. Kinetic: The power supply causes all charges in the circuit
to speed up at the same time, and energy is injected into the entire
circuit. (Imagine speeding up a flywheel by repeatedly brushing your
hand against its rim.) The load extracts energy from the circuit by
opposing the flow of charge and decellerating all the charges in the
circuit (think of slowing down a flywheel by allowing it to rub
against your hand). Both processes occur simultaneously: the
source injects energy while the load extracts it, and energy
flows from source to load. This might be hard to discover by
observing such a circuit in DC operation, since the entire loop of
charges is being sped up and slowed down simultaneously, and so
remains at a constant current throughout the circuit.
2. Potential: The power supply pulls negative charges from one
wire of the circuit and injects them into the other. This
creates separation of charge, increasing potential difference,
and the whole circuit acts like a capacitor. (Think of an air
pump sucking air from one sealed pipe and pushing it into another.)
By moving the charges between wires, the power supply injects energy
into this "capacitor." At the same time, the bulb allows charges to
leak back down the potential hill. It extracts energy from the
circuit, and the capactitor is gradually discharged. (think of a
turbine motor connected between the pipes, with its rotation driven by
the flow created by pressure difference.) Both processes occur
simultaneously, the power supply injects energy while the load
extracts it, and energy flows from source to load. This might be hard
to discover through observation, since the potential is raised and
lowered simultaneously, and so remains at a constant potential
difference throughout the circuit.
> is almost meaningless.
"Electric energy" has a very tight definition: it is electromagnetic
energy composed of E x M. "Electric energy" includes light and radio
waves, and also includes the energy which propagates from generator to
light bulb. When an AC generator produces EM energy and your electric
heater consumes it, electromagnetic energy is flowing along the circuit
from generator to load. Any textbook on EM waves and waveguides will
describe the physics. What works at 1MHz will apply just the same at
> There is the energy in the circuit (previous statement), and there is
> the energy in an E-M field. The E-M field energy is not the kinetic
> energy of the current carriers.
True, yet I must totally disagree with you on this point. The energy in a
circuit *IS* the energy of the electromagnetic field. Kinetic energy of
charge carriers is incredibly tiny, and it does not enter into
explanations of circuitry. Refer to a basic textbook on EM Waves. Energy
in a circuit is composed of EM fields. (If electrons had no charge, only
then would the energy propagate as electron KE.) But energy in circuits
propagates as EM fields. Quantity of energy moving in circuits can be
calculated if the potential difference and charge flow is known. It can
also be calculated using Poynting Vectors if the complete e-fields and
b-fields surrounding the wires are known. But note well: if all you know
is the KE of electrons, then you cannot calculate the net energy transport
through a circuit.
> The term "electric energy" is almost meaningless.
Perhaps instead I should have said "electromagnetic energy"? This term is
not meaningless, since the electric energy that propagates through a
simple circuit is identical to the "stuff" we usually call radio waves,
but it has much lower frequency, and it is using the wires as a waveguide.
Perhaps you're thinking of the common idea that "energy" is an abstract
concept. On this we agree. But while the term "energy" refers to no real
"stuff," the same is not true of terms like "acoustical energy" or
"optical energy." Sound and light are not merely abstract concepts! The
same is true of radio waves: they're real, they aren't just abstract
concepts. The same is true of the electromagnetic energy which propagates
along a pair of 60Hz wires. That "electrical energy" is just as real as
sound, or radio waves, or light.
Thought experiment: consider a coaxial waveguide with microwave radiation
propagating inside. (Note that *coax* waveguides are typically much
smaller diameter than wavelength of the propagating waves.) Don't you
agree that the propagating energy is composed of EM fields within the
waveguide? Now imagine that the frequency of the radiation is reduced.
The wavelength increases, yet the fundamental characteristics of the
system are not altered: the propagating energy is still composed of
electromagnetic fields propagating at the speed of light. Now imagine
that the frequency is reduced to 60Hz. The general public calls this
energy "electricity", yet it's identical to microwave radiation (although
much lower in frequency). If microwave energy in a waveguide is
progressively reduced in frequency, there is no special threshold at which
the EM energy changes from propagating radiation and turns into
"electricity". A coaxial waveguide can transport 60Hz energy as easily as
it does 10GHZ microwave energy. Even if the frequency is reduced to zero
(a DC system), the propagating energy is still contained entirely in the
EM fields, and travels at nearly the speed of light, and can be calculated
by integrating the E X B throughout the volume within the waveguide.
Yes, electrons are important; they couple the EM fields to the physical
circuit, and they force the propagating EM to remain within the waveguide
and not radiate into space. They do this for coaxial waveguides and for
two-wire waveguides, and this effect is independent of frequency. The AC
cord of a 120v floor lamp is a waveguide for 60HZ energy, and this energy
is contained in the EM fields surrounding the pair of wires.
> ELECTRIC POWER CANNOT BE MADE TO FLOW Power is defined as "flow of
> energy" - NOT TRUE.
> Power is not a material thing
> (neither is energy). In that sense neither of them "flows". They are
> really both abstract concepts since energy is really an abstract
> concept! Your other statements like "electric power is an energy
> current" is nonsensical.
I agree that "pure energy" is an abstract concept. But the concept of
energy" in circuits is quite different. It's no different than beams of
and radio waves. Is a beam of light nothing except an abstract concept?
Of course not. True, it's not a material thing, but it carries mass and
it behaves as a "stuff" in the same way that light and RF radiation is a
"stuff". If electrical energy is just an abstract concept, then we'd be
forced to say that sound and light are merely abstract concepts. Think
like this: light is electromagnetic energy, so must we say that, because
light is energy, and because energy is 'merely' an abstract concept,
therefore light is merely an abstract concept and does not "really exist?"
Of course not. On the contrary, light exists, and so does the
electromagnetic energy which flows within an operating electrical circuit.
Here's where you're getting confused: "pure energy" is an abstract
concept, but light and RF radiation is not, and neither is the EM energy
which flows across an electric circuit. Each joule of EM energy provided
by an electric generator can be located. Each joule of EM energy flows at
nearly the speed of light between generator and distant load.
> Power is the instantaneous time rate of change of energy (it is a
> calculus derivative).
True, but in EM wave mechanics, power is also the expression of the rate
at which each electromagnetic energy propagates. This concept applies to
circuits, but also applies to EM waves in general: Imagine an optical
fiber with bright light of constant intensity passing along it. There is
no time rate of change of energy in the fiber because the intensity is
constant throughout. However, because the light is MOVING, it has a
particular propagation rate, and hence a net energy flow rate. A specific
volume of this light, having particular intensity, has a specific energy.
When this particular "chunk" of light moves along, its flow rate can be
expressed in terms of power; in terms of the quantity of energy moving
over a unit of time. An optical fiber is like a hose which delivers
joules of EM energy instead of gallons of water, and where the flow rate
of this energy is expressed in joules per second (watts) rather than
gallons per second.
All of this applies to circuits, since EM fields propagating through an
optical fiber are, except for frequency, identical to EM fields
propagating within a metal waveguide, or propagating along a pair of
wires. The phenomena are independent of frequency. A pair of wires is a
"hose" for electromagnetism.