In wires, where does the energy flow? Does it move along w/electrons? Hmmm.
1997 W. Beaty


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".
> 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:

> > 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 cm/sec velocities.

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 energy 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 all 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 medium.

> 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 electrons, 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 magnetism, but this energy remains in one place and does not propagate from source to load.

Two ways to visualize the energy flow in a circuit:

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.

> ELECTRIC CURRENT IS NOT A FLOW OF ENERGY - The term "electric energy"
> 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 60Hz.

> 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 "electromagnetic energy" in circuits is quite different. It's no different than beams of light 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.


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