# Is the Poynting Vector Field the Only Factor in Energy Flow in Circuits?

• I
• Dario56
Dario56
In a simple circuit consisting of a battery and a resistor, current will flow if the circuit is closed. Resistor uses the energy provided by the battery, creating heat with a power ##P = UI##, where ##U## is a voltage across the resistor and ##I## is a current through the resistor.

In my classical physics classes, I learned that resistors create heat because of collisions between free electrons and atoms in the crystal lattice of the conductor. Electrons accelerated by the electric field in the conductor, dissipate their kinetic energy as heat. However, in the Science Asylum video on YouTube: Circuit Energy doesn't FLOW the way you THINK!, it was argued that the energy provided to the electrons by the electric field isn't the energy that powers the circuit components, but rather that the fields around the circuit power them. This is explained with the Poynting vector field around the circuit where it is clear that the energy flows from the battery to the resistor.

While that makes sense, it doesn't really explain the mechanism by which the heat is created, it just explains the direction of energy flow and how it relates to electric and magnetic fields. Furthermore, it seems that this explanation is misleading as heat on the resistor can't be magically created by the fields around the circuit, flow of electrons and their interaction with the lattice is a crucial part of how the heat is created on the resistor (if my understanding is correct). Without this interaction, resistor wouldn't create heat, but some other form of energy. Therefore, acceleration of electrons in the electric field is important and it does power the resistor (in the classical view). Also, in the Poynting vector field, it can be seen that inside the conductor, energy flow goes from the outside towards the conductor which I think essentially describes the acceleration of electrons in the electric field.

In another example, LED creates energy in the form of light with much less heat because the mechanism of its operation is quite different compared to the resistor (classical light bulb).

Poynting vector field is very similar in both cases and in both cases, energy flows from the battery to the circuit element. However, Poynting vector by itself can't explain what energy form is created by the circuit element (its different with the resistor and the LED), that has to do with its operation principle.

Last edited:
Dario56 said:
it doesn't really explain the mechanism by which the heat is created
Correct. Poynting’s theorem says that whenever ##\vec J \cdot \vec E \ne 0## there will be a transfer of energy from the fields to the matter. It does not distinguish between any different mechanisms. So it doesn’t distinguish between transfers to chemical potential, mechanical work, heat or anything else. All it tells you is that energy has transferred between the fields and the matter.

Dario56 said:
Furthermore, it seems that this explanation is misleading as heat on the resistor can't be magically created by the fields around the circuit, flow of electrons and their interaction with the lattice is a crucial part of how the heat is created on the resistor (if my understanding is correct).
There is nothing misleading about it. It is correct. It just doesn’t make any claims about mechanisms

cianfa72
Your point is completely valid and I do not mean to detract from it at all, but just FYI, your example of a resistor
Dario56 said:
resistor (classical light bulb)
is a bad one because a light bulb is not a normal resistor at all. It has a varying response to voltage as it heats up whereas normal resistors don't do that (to any significant degree).

Dario56
The energy appears where the Poynting vector ends by entering the circuit element material. For a resistor in a simple single circuit, the current is the same everywhere, but the voltage dropped is proportional to resistance.

Energy is delivered to where the voltage is dropped, that determines the power distribution in the circuit. Power, W = V * I; Most Poynting vectors terminate in the load, where most of the circuit voltage drop occurs.

A few Poynting vectors enter and terminate inside the circuit wires, so the resistive wires do produce some heat. Thicker wires drop less voltage, so terminate fewer Poynting vectors, and stay cooler.

cianfa72
Dale said:
Correct. Poynting’s theorem says that whenever ##\vec J \cdot \vec E \ne 0## there will be a transfer of energy from the fields to the matter. It does not distinguish between any different mechanisms. So it doesn’t distinguish between transfers to chemical potential, mechanical work, heat or anything else. All it tells you is that energy has transferred between the fields and the matter.

There is nothing misleading about it. It is correct. It just doesn’t make any claims about mechanisms
I think that it's misleading to stay that energy provided to electrons isn't the energy that powers the circuit elements and this is what is claimed in the video.

As I said, electric field from the battery, accelerates electrons whose kinetic energy is turned into heat in a resistor. Energy provided to electrons is what creates power. Poynting vector certainly holds, but without energy provided to electrons, heat couldn't form.

Dario56 said:
As I said, electric field from the battery, accelerates electrons whose kinetic energy is turned into heat in a resistor. Energy provided to electrons is what creates power. Poynting vector certainly holds, but without energy provided to electrons, heat couldn't form.
That is very wrong.

The electric field between the wires comes from the battery voltage. The current that flows to charge the line, supports a guided magnetic wave along the line, in phase with the voltage. The cross product of those electric and magnetic fields is the Poynting vector. That is sufficient to explain all the energy flow along the line.

The guided magnetic field causes a proportional current in the wire. We can measure the strength of the electric field, as the voltage between the wires. The product of line voltage and line current is power, and is exactly equal to the sum of all the Poynting vectors.

cianfa72
Baluncore said:
That is very wrong.

The electric field between the wires comes from the battery voltage. The current that flows to charge the line, supports a guided magnetic wave along the line, in phase with the voltage. The cross product of those electric and magnetic fields is the Poynting vector. That is sufficient to explain all the energy flow along the line.

The guided magnetic field causes a proportional current in the wire. We can measure the strength of the electric field, as the voltage between the wires. The product of line voltage and line current is power, and is exactly equal to the sum of all the Poynting vectors.
That is true, but it doesn't explain how heat is created in a resistor and why does LED produce mostly light. My point is, Poynting vector does explain where the energy goes and the amount produced, but it doesn't explain what type of energy is created and how.

Poynting vector doesn't know anything about the interaction of electrons with the crystal lattice which is crucial to explain why specifically heat is produced in the resistor and not some other form of energy. Without the electric field accelerating the electrons which interact with the lattice, heat wouldn't be produced.

Dario56 said:
My point is, Poynting vector does explain where the energy goes, but it doesn't explain what type of energy is created and how.
That is decided by the devices you connect to the line. How and where the voltage is dropped decides how much energy is delivered. You need to study those different circuit elements, if possible, divorced from the supply line.

Baluncore said:
That is decided by the devices you connect to the line. How and where the voltage is dropped decides how much energy is delivered. You need to study those different circuit elements, if possible, divorced from the supply line.
Yes, exactly. That's why when Science Asylum claims that energy which electrons get from the source don't power the circuit elements is misleading. The fact that electric field exists around the circuit and current flows (magnetic field) by itself doesn't explain how the resistor gets hot. They don't magically create heat.

It's precisely the kinetic energy provided by the electric field to the electrons and its dissipation that explains the heat.

Dario56 said:
In a simple circuit consisting of a battery and a resistor, current will flow if the circuit is closed. Resistor uses the energy provided by the battery, creating heat with a power ##P = UI##, where ##U## is a voltage across the resistor and ##I## is a current through the resistor.

In my classical physics classes, I learned that resistors create heat because of collisions between free electrons and atoms in the crystal lattice of the conductor. Electrons accelerated by the electric field in the conductor, dissipate their kinetic energy as heat. However, in the Science Asylum video on YouTube: Circuit Energy doesn't FLOW the way you THINK!, it was argued that the energy provided to the electrons by the electric field isn't the energy that powers the circuit components, but rather that the fields around the circuit power them. This is explained with the Poynting vector field around the circuit where it is clear that the energy flows from the battery to the resistor.

While that makes sense, it doesn't really explain the mechanism by which the heat is created, it just explains the direction of energy flow and how it relates to electric and magnetic fields. Furthermore, it seems that this explanation is misleading as heat on the resistor can't be magically created by the fields around the circuit, flow of electrons and their interaction with the lattice is a crucial part of how the heat is created on the resistor (if my understanding is correct). Without this interaction, resistor wouldn't create heat, but some other form of energy. Therefore, acceleration of electrons in the electric field is important and it does power the resistor (in the classical view). Also, in the Poynting vector field, it can be seen that inside the conductor, energy flow goes from the outside towards the conductor which I think essentially describes the acceleration of electrons in the electric field.

In another example, LED creates energy in the form of light with much less heat because the mechanism of its operation is quite different compared to the resistor (classical light bulb).

Poynting vector field is very similar in both cases and in both cases, energy flows from the battery to the circuit element. However, Poynting vector by itself can't explain what energy form is created by the circuit element (its different with the resistor and the LED), that has to do with its operation principle.

Maybe, the following articles might be of help:

Energy transfer in electrical circuits: A qualitative account
Igal Galili and Elisabetta Goihbarg
Am. J. Phys. 73, 141 (2005); doi: 10.1119/1.1819932

Understanding Electricity and Circuits: What the Text Books Don’t Tell You
Ian M. Sefton
Science Teachers’ Workshop 2002

Energy flow from a battery to other circuit elements: Role of surface charges
Manoj K. Harbola
American Journal of Physics 78, 1203 (2010); doi: 10.1119/1.3456567

vanhees71 and Dale
Dario56 said:
I think that it's misleading to stay that energy provided to electrons isn't the energy that powers the circuit elements and this is what is claimed in the video
What are you talking about? The energy provided to the electrons is provided according to Poynting’s theorem. That energy does power the circuit elements.

Poynting’s theorem is about energy and electromagnetic fields. It describes how the electromagnetic field gains energy from matter, contains energy, moves energy, and loses energy to matter. That is all it claims, but it does claim and correctly describe that.

What it does not describe is what the matter does with that energy once it leaves the fields. It does describe the energy transfer from the fields into a resistor or a charging battery. It does not tell you if the matter receiving the energy is using it to produce heat or to produce chemical potential.

Dario56 said:
As I said, electric field from the battery, accelerates electrons whose kinetic energy is turned into heat in a resistor. Energy provided to electrons is what creates power. Poynting vector certainly holds, but without energy provided to electrons, heat couldn't form.
Poynting’s theorem describes the energy provided to the electron. There is no separate energy provided to the electrons than what is described in Poynting’s theorem. That is the energy that then is used by the electrons to produce the heat.

cianfa72 and nasu
Dario56 said:
That is true, but it doesn't explain how heat is created in a resistor and why does LED produce mostly light. My point is, Poynting vector does explain where the energy goes and the amount produced, but it doesn't explain what type of energy is created and how.
That is correct. Nor does it claim to do so. There is nothing misleading about a theorem saying what it says and not saying things that it doesn’t say. I wholly object to your characterization that this is in any way misleading.

Would you consider it proper, in this context, for me saying that you are being misleading because you didn’t distinguish between wage income and adjusted gross income here in this thread? Of course not, that isn’t the topic of the thread. Similarly, what the matter does with the energy provided by the fields is not the topic of Poynting’s theorem. There is nothing misleading about that.

Dario56 said:
Poynting vector doesn't know anything about the interaction of electrons with the crystal lattice which is crucial to explain why specifically heat is produced in the resistor and not some other form of energy.
True. That does not make it misleading.

Dale said:
What it does not describe is what the matter does with that energy once it leaves the fields. It does describe the energy transfer from the fields into a resistor or a charging battery. It does not tell you if the matter receiving the energy is using it to produce heat or to produce chemical potential.
Exactly, that's what I'm claiming
What are you talking about? The energy provided to the electrons is provided according to Poynting’s theorem. That energy does power the circuit elements.
I agree, but that's not what is claimed in the YouTube video from Science Asylum: Circuit Energy doesn't FLOW the way you THINK!. I think he probably meant to say the same thing we claim, but he phrased it poorly. I'm quoting what he said (2:03):
''The charged particles do have energy because, well, everything has energy, but that's not the energy that's powering whatever device you're using.''
And I disagree with this statement as energy from the EM field is received by the electrons and then dissipated as heat (in the resistor, not the case in LED). In that sense, kinetic energy of electrons powers the resistor as they are accelerated in the electric field. Without it, no heat can be created.

Oh, you are saying that some random You Tube video is misleading, not that Poynting’s theorem is misleading.

Sorry about misunderstanding. And sorry about posting. I shouldn’t have gotten involved then.

Dale said:
Oh, you are saying that some random You Tube video is misleading, not that Poynting’s theorem is misleading.

Sorry about misunderstanding. And sorry about posting. I shouldn’t have gotten involved then.
Yep, this guy is really good and his videos are top. Here, I think he does give some misleading statements, but I'm glad you gave your answers because it showed me that my thinking was correct. In that sense, I'm glad you joined the discussion.

Dale said:
What are you talking about? The energy provided to the electrons is provided according to Poynting’s theorem. That energy does power the circuit elements.

Poynting’s theorem is about energy and electromagnetic fields. It describes how the electromagnetic field gains energy from matter, contains energy, moves energy, and loses energy to matter.
Sorry to resume this thread. For the case in which the electromagnetic field gains energy from matter, do you mean when ##\vec J \cdot \vec E \lt 0## ?

cianfa72 said:
Sorry to resume this thread. For the case in which the electromagnetic field gains energy from matter, do you mean when ##\vec J \cdot \vec E \lt 0## ?
Yes, for example in a battery. The E field points from the positive terminal to the negative terminal, and the current goes from the negative terminal to the positive terminal. So ##\vec J \cdot \vec E## is negative and the electromagnetic field is gaining energy from the battery.

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