Electromagnetic Induction vs. Electromagnetic Radiation

[KhalDirth]

So, I have a few questions regarding some of the laws of electromagnetism.

While I was in school, one of my classes was Electrodynamics (as an ECE undergrad). We discussed how a current through a conductor creates both magnetic and electric fields (Maxwell's equations, among others, were used to determine strength/direction/gradient/densities etc.).

I understand how magnetic induction works. What I do not entirely understand is radiation. It seems to me that a radio transmitter is a device with an alternating source of radio frequency. In my mind, this would create an alternating magnetic field. This could be used for wirelss communication (this type of device was precurser to the modern-day radio) at small distances.

I have read that the radiation element of a transmitter comes from the electrons accelerating. A 10kHz sinewave is a constant speed. Velocity might change for the electron, true, but I cannot see how taking a stationary electron and moving it down a wire at the speed of light will produce photons of varying frequencies. What are the equations that relate the frequency of the source to the frequency of the photon?

Am I to assume that any alternating source is giving off EM radiation as well as inductive forces? If so, then I don't understand how a 60 Hz lightbulb can emit radiation at the Terahertz level. To me, it would seem to give an electromagnetic field of 60 Hz as well as radiated photons with a frequency of 60 Hz. (Is thermal emission different from typical EM radiation?). Would it be possible to produce light from a Terahertz-scale oscillator?

I understand this is a lengthy post, but lacking a deeper physics background, I feel ungrounded in this area.

Cheers,
Mario

 

[Born2bwire]

It is all based on Maxwell's equations. They state that a time-varying current will produce time-varying electric and magnetic fields. These fields, once generated, do not need the source current to propagate, they can become unguided waves and go off into free-space like any radio signal.

A more basic concept is that any accelerating charge will give off radiation. Under this assumption, we see that time-varying currents are nothing more than a macroscopic series of charges undergoing constant acceleration.

The limitation with Maxwell's equations is that it is a purely classical theory. It does have the advantage that it follows special relativity so its extension goes beyond other classical theories like Newtonian physics. However, it does not predict photons or the quantization of the electric and magnetic fields. As such, for frequencies in the Terahertz range and higher it is generally better to use quantum electrodynamics. A classical antenna that would emit visible light waves is unobtainable. Both an oscillator of that high frequency and a resonant antenna structure are physically impossible to create. A resonant antenna is of the size on the order of the wavelength of the desired signal. This means that a classical visible light antenna would be on the order of 100 nanometers. However, we can explain the function of a light bulb using the black body radiator theory, which relies on quantum electrodynamics. The light is emitted because the heating of the wire element causes phonon vibration modes. The phonons can emit photons, the general power spectrum being predicted by the black body radiator (approximately since the black body is an idealization).

 

[KhalDirth]

It is all based on Maxwell's equations. They state that a time-varying current will produce time-varying electric and magnetic fields. These fields, once generated, do not need the source current to propagate, they can become unguided waves and go off into free-space like any radio signal.

A more basic concept is that any accelerating charge will give off radiation. Under this assumption, we see that time-varying currents are nothing more than a macroscopic series of charges undergoing constant acceleration.

The limitation with Maxwell's equations is that it is a purely classical theory. It does have the advantage that it follows special relativity so its extension goes beyond other classical theories like Newtonian physics. However, it does not predict photons or the quantization of the electric and magnetic fields. As such, for frequencies in the Terahertz range and higher it is generally better to use quantum electrodynamics. A classical antenna that would emit visible light waves is unobtainable. Both an oscillator of that high frequency and a resonant antenna structure are physically impossible to create. A resonant antenna is of the size on the order of the wavelength of the desired signal. This means that a classical visible light antenna would be on the order of 100 nanometers. However, we can explain the function of a light bulb using the black body radiator theory, which relies on quantum electrodynamics. The light is emitted because the heating of the wire element causes phonon vibration modes. The phonons can emit photons, the general power spectrum being predicted by the black body radiator (approximately since the black body is an idealization).

I am still a bit confused. These time-varying fields exist in orientation around the current (such as in an inductor). Maxwell's equations predict their orientation and magnitude in three dimensional space. So you must be saying that Maxwell's equations can't predict how radiation (in the form of photons) will occurr. Also, it is my understanding that radiowave transmission makes use of radio-frequency photon emission to travel long distances, not the aforementioned electromagnetic fields predicted by Maxwell's equations (B-fields and the like), as a B-field deteriorates rather quickly over distance.

 

[Bob_for_short]

The current frequency is usually constant in low radio-wave diapason (LW, MW, SW). The variable electromagnetic field around antenna can be decomposed into two terms: a "near" filed that vanishes quickly with distance (a dipole field "attached" to the antenna) and a radiated field that propagates far away and vanishes as 1/r². The radiated wave has the same frequency as the antenna. This follows from the Maxwell equations. At far distances only radiated wave "survives" (dominates).

 

[Born2bwire]

No, Maxwell's equations say nothing about photons, photons are entirely in the domain of quantum mechanics. However, the observable of the photon in quantum electrodynamics is the electric and magnetic field. So while the photon (technically we talk about the scalar and vector potentials as being the basic elements of electromagnetic fields) is the... ummm... "basic primitive" of the electromagnetic fields, the actual observables are the electric and magnetic fields.

So the macroscopic limit of quantum electrodynamics is always the classical Maxwell equations. So any macroscopic electromagnetic phenomonon that is in frequencies below the Terahertz range can pretty much be predicted entirely by Maxwell's equations. There is still a huge bevy of research in classical electromagnetics despite the theory being around for over a hundred years. That's how I make my paycheck at least.

The next point is that a proper antenna creates time-varying electric and magnetic fields. The electromagnetic wave is not simply the magnetic field, but contains an electric field component as well. Under these auspices, the wave will only fall off in a lossless medium due to spatial loss. That is, if I was to send out a signal uniformly in all directions, we can imagine the wavefront as a spherical shell. The total power/energy contained in the surface of this shell in the wave stays the same. As the wave travels out, since it travels in the same speed in all directions, the shell expands uniformly and stays spherical. But since no energy is dissipated in a lossless medium, the energy contained on the surface must stay the same. So the energy must fall off as 1/r^2, known as the inverse square law (or space loss factor). This is the same drop off as gravity and so we can see by the analogue of gravity that electromagnetic radiation is a far-reaching effect.

 

[KhalDirth]

No, Maxwell's equations say nothing about photons, photons are entirely in the domain of quantum mechanics. However, the observable of the photon in quantum electrodynamics is the electric and magnetic field. So while the photon (technically we talk about the scalar and vector potentials as being the basic elements of electromagnetic fields) is the... ummm... "basic primitive" of the electromagnetic fields, the actual observables are the electric and magnetic fields.

So the macroscopic limit of quantum electrodynamics is always the classical Maxwell equations. So any macroscopic electromagnetic phenomonon that is in frequencies below the Terahertz range can pretty much be predicted entirely by Maxwell's equations. There is still a huge bevy of research in classical electromagnetics despite the theory being around for over a hundred years. That's how I make my paycheck at least.

The next point is that a proper antenna creates time-varying electric and magnetic fields. The electromagnetic wave is not simply the magnetic field, but contains an electric field component as well. Under these auspices, the wave will only fall off in a lossless medium due to spatial loss. That is, if I was to send out a signal uniformly in all directions, we can imagine the wavefront as a spherical shell. The total power/energy contained in the surface of this shell in the wave stays the same. As the wave travels out, since it travels in the same speed in all directions, the shell expands uniformly and stays spherical. But since no energy is dissipated in a lossless medium, the energy contained on the surface must stay the same. So the energy must fall off as 1/r^2, known as the inverse square law (or space loss factor). This is the same drop off as gravity and so we can see by the analogue of gravity that electromagnetic radiation is a far-reaching effect.

Let's see if I understand what you're saying. You're saying that the electric and magnetic field lines predicted by classical electrodynamics are analogous to the quantum predicted waves? I was unaware that time-varying fields travelled. Or, in your spherical thought experiment, are you saying that the field lines are still oriented on your antenna, and that they weaken in the same manner that gravity weakens with the inverse square law.

If I am interpretting this correctly, then what is the difference between radio type communication and Nathan Stubblefield's frequency induction?

http://en.wikipedia.org/wiki/Nathan_Stubblefield

It seems to me that the only difference is that the field lines of a radio source extend far past those of an audio frequnecy source.

 

[Born2bwire]

Induction is more of a near-field property. It is primarily done through the changing magnetic field coupling through say a loop of wire. For the most part, it isn't very different but the conditions for inductive coupling to occur are very general and just obtaining coupling does not guarantee efficient power transfer.

As Bob mentioned, there are various regions to a radiating antenna. The volume closely surrounding the antenna is known as the near field. If you recall in circuit theory, if we have a net reactive impedance in a circuit, either inductive or capacitive, it creates a phase difference between the current and voltage. This splits the power in the circuit between real and reactive power. The reactive power exists because the voltage and current do not peak at the same time, so the actual power that we can draw out is less than the ideal maximum. Some energy sloshes about the circuit without being absorbed.

In an analagous line of thought, the near-field is a reactive power field. A portion of the antenna's fields get trapped locally in what is called the near field. These fields do not contribute to the propagating fields, they die out very quickly, 1/r at the slowest generally. Far from the antenna we have the far-field (also called the Fraunhofer region), here we only have the propagating waves.

Now to efficiently capture the radiation, we need to make antennas that are specially designed to direct power along a very narrow volume of space (instead of all over willy-nilly) and we need it to be resonant at the desired frequencies. All of these implications are generall ignored when it comes to simple inductive coupling. Inductive coupling is the coupling of elements with their near fields, not the far fields (although the physics are basically the same).

We can use any frequency below Terahertz to make and receive electromagnetic waves. We can certainly do audio frequencies and below, the only problem is that the wavelength is so bloody long it is very difficult to make a resonant structure of such large size. Take a look at the ELF submarine antennas (extremely low frequency). The ELF antennas were made to communicate with the Navy's nuclear subs and are huge, 20-40 km in size.

 

[Born2bwire]

Oh another major difference between induction is that since induction relies on the magnetic fields, the receiver and transmitter designs are more limited than a true antenna. An antenna can be designed to react with either the electric or magnetic fields of the wave. The typical wire antenna that you have seen (called a whip antenna or a quarter-wavelength monopole antenna) is designed so that it primarily reacts to the electric field in the wave. The length of the wire needs to be aligned with the electric field of the receiving wave to achieve maximum reception. And vice-versa, the wave generated by such a wire antenna (ie: dipole or monopole antenna) has its electric field aligned along the length of the wire antenna. If we want to couple primarily to the magnetic field, we would use a loop of wire. Of course there are a whole range of different designs and they are not limited to wire antennas and the other field component still has an impact as well.

 

[KhalDirth]

Induction is more of a near-field property. It is primarily done through the changing magnetic field coupling through say a loop of wire. For the most part, it isn't very different but the conditions for inductive coupling to occur are very general and just obtaining coupling does not guarantee efficient power transfer.

As Bob mentioned, there are various regions to a radiating antenna. The volume closely surrounding the antenna is known as the near field. If you recall in circuit theory, if we have a net reactive impedance in a circuit, either inductive or capacitive, it creates a phase difference between the current and voltage. This splits the power in the circuit between real and reactive power. The reactive power exists because the voltage and current do not peak at the same time, so the actual power that we can draw out is less than the ideal maximum. Some energy sloshes about the circuit without being absorbed.

In an analagous line of thought, the near-field is a reactive power field. A portion of the antenna's fields get trapped locally in what is called the near field. These fields do not contribute to the propagating fields, they die out very quickly, 1/r at the slowest generally. Far from the antenna we have the far-field (also called the Fraunhofer region), here we only have the propagating waves.

Now to efficiently capture the radiation, we need to make antennas that are specially designed to direct power along a very narrow volume of space (instead of all over willy-nilly) and we need it to be resonant at the desired frequencies. All of these implications are generall ignored when it comes to simple inductive coupling. Inductive coupling is the coupling of elements with their near fields, not the far fields (although the physics are basically the same).

We can use any frequency below Terahertz to make and receive electromagnetic waves. We can certainly do audio frequencies and below, the only problem is that the wavelength is so bloody long it is very difficult to make a resonant structure of such large size. Take a look at the ELF submarine antennas (extremely low frequency). The ELF antennas were made to communicate with the Navy's nuclear subs and are huge, 20-40 km in size.

Does classical electrodynamics predict these waves? I never studied them in school. I can grasp only so much of what you say, as the idea of a near-field, wherein electric potential is fluctuating, seems so much different from a wave that is travelling. Or am I confusing the idea of an alternating electric field that exists far beyond the near field with some soft of pulsed longitudinal wave? Maybe my idea of a wave is confused.

By the way, I've actually done ELF research before (though of a very different nature), wherein I designed a seismic communication system that utilized a 1 kWatt speaker and a geoprobe (with proprietary filtering and DSP) to obtain a signal.

 

[Born2bwire]

Oh yes. Pretty much the entirety of classical electrodynamics comes from just five equations. The four equations of Maxwell's equations and the Lorentz force which relates to force on a charge due to electric and magnetic fields. That's it, that's pretty much the entire basis of electromagnetics (with electrostatics being a subset of electromagnetics (or electrodynamics if you like)).

For most intents and purposes, it is not possible to have a longitudinal electromagnetic wave. In a source-free homogeneous region, you can only have transverse waves. The propagating waves are transverse waves. Now, exceptions can be made if we have in inhomogeneous region, a lot of surface waves are longitudinal. And confined waves can also be longitudinal, but often times it is a fake longitudinal. That is, the waves are still transverse but the superposition of them from their reflections make the total field longitudinal (but once you think about it in a causal sense you are forced to decompose it into transverse waves). The other common exception is when you are in a region that contains a source, like the volume around an antenna. These longitudinal waves are the near-field waves. Now, some transverse components can also be in the near-field terms but any longitudinal waves must be near-field (since far away we can approximate space to be source-free and thus must only have transverse waves).

It may be easier to think about an AC circuit. Any AC circuit propagates its signals using electromagnetic waves. The transmission of the signal between elements is done only by electromagnetic waves. But in a circuit, these waves are guided waves, the traces on a PCB or the wires of our circuit guide the waves along the desired path. An antenna is a transformer of sorts. The antenna is a device that transforms guided electromagnetic waves into propagating electromagnetic waves (and vice-versa). So all it is doing is taking the guided wave that is sent to the antenna and providing it a means of going into open space. In fact, at patch antenna is a good direct approximation of this. A patch antenna sets of a sort of resonant cavity for the guided waves but has open sides. That is, the guided wave flows between the microstrip line (the PCB trace on top of a board) and the ground plane (the copper sheet on the bottom of the board) into the patch antenna (nothing more than a copper square on the top that the microstrip is attached to). The patch antenna traps the guided wave so that it bounces back and forth in a kind of parallel plate cavity. The open sides allow the wave to "leak out" into open space. Another good example is a horn antenna, which takes a rectangular waveguide and slowly expands it out so that it gradually widens up into "open" space.

A look at the wikipedia articles on electromagnetics and antennas may provide some better basic explanations.

 

[KhalDirth]

Oh yes. Pretty much the entirety of classical electrodynamics comes from just five equations. The four equations of Maxwell's equations and the Lorentz force which relates to force on a charge due to electric and magnetic fields. That's it, that's pretty much the entire basis of electromagnetics (with electrostatics being a subset of electromagnetics (or electrodynamics if you like)).

For most intents and purposes, it is not possible to have a longitudinal electromagnetic wave. In a source-free homogeneous region, you can only have transverse waves. The propagating waves are transverse waves. Now, exceptions can be made if we have in inhomogeneous region, a lot of surface waves are longitudinal. And confined waves can also be longitudinal, but often times it is a fake longitudinal. That is, the waves are still transverse but the superposition of them from their reflections make the total field longitudinal (but once you think about it in a causal sense you are forced to decompose it into transverse waves). The other common exception is when you are in a region that contains a source, like the volume around an antenna. These longitudinal waves are the near-field waves. Now, some transverse components can also be in the near-field terms but any longitudinal waves must be near-field (since far away we can approximate space to be source-free and thus must only have transverse waves).

It may be easier to think about an AC circuit. Any AC circuit propagates its signals using electromagnetic waves. The transmission of the signal between elements is done only by electromagnetic waves. But in a circuit, these waves are guided waves, the traces on a PCB or the wires of our circuit guide the waves along the desired path. An antenna is a transformer of sorts. The antenna is a device that transforms guided electromagnetic waves into propagating electromagnetic waves (and vice-versa). So all it is doing is taking the guided wave that is sent to the antenna and providing it a means of going into open space. In fact, at patch antenna is a good direct approximation of this. A patch antenna sets of a sort of resonant cavity for the guided waves but has open sides. That is, the guided wave flows between the microstrip line (the PCB trace on top of a board) and the ground plane (the copper sheet on the bottom of the board) into the patch antenna (nothing more than a copper square on the top that the microstrip is attached to). The patch antenna traps the guided wave so that it bounces back and forth in a kind of parallel plate cavity. The open sides allow the wave to "leak out" into open space. Another good example is a horn antenna, which takes a rectangular waveguide and slowly expands it out so that it gradually widens up into "open" space.

A look at the wikipedia articles on electromagnetics and antennas may provide some better basic explanations.

Well, I always thought of current in the charge-carrying sense. That is, electric current has its hydrodynamic analog, and instead of water molecules, we have holes or electrons moving (depending upon current convention used). I also have always thought of electric and magnetic fields as lines of force, gradients in which electric or magnetic potential changed with respect to position of the moving current. So, to me, this way of thinking is new. I suppose I will have to fix it.

Wikipedia is a good place to start, but I definitely prefer the widsom of professionals.

 

[Born2bwire]

Well, when it comes to enquiring about the basics of a very broad subject such as this, it is probably preferable to consult a textbook or other formal resource (a good text is by David Griffiths, that's what I used in my physics courses). We are a good resource at explaining specific things but I think that you will find a more organized and complete answer in a reference. I'm just writing all of this off the cuff so the organization, completeness, and level of complexity in the explanations leave something to be desired.

 

[KhalDirth]

Well, when it comes to enquiring about the basics of a very broad subject such as this, it is probably preferable to consult a textbook or other formal resource (a good text is by David Griffiths, that's what I used in my physics courses). We are a good resource at explaining specific things but I think that you will find a more organized and complete answer in a reference. I'm just writing all of this off the cuff so the organization, completeness, and level of complexity in the explanations leave something to be desired.

Actually, I remember a number of the physics students at my college carrying the Griffiths book around. I recognize it by its front cover. I will look into purchasing it.

 

[Born2bwire]

Actually, I remember a number of the physics students at my college carrying the Griffiths book around. I recognize it by its front cover. I will look into purchasing it.

He actually has three textbooks though I never looked at his particle book. He has another textbook on quantum mechanics that I used too (has a wonderful cover, living cat on the front, dead cat on the back, Oh Professor Griffiths, how you jest). Though I think feelings are a bit mixed on his quantum book since there are a number of other really good references too (everyone has their favorite, usually the one that they were taught with). My electrical engineering course on electromagnetics has slides and applets up on the professor's website.

www.amanogawa.com

I still use it as a quick reference and the applets are handy in a pinch, I've used them on the job. My graduate level electrical engineering course on electromagnetics used a text from Constantine Balanis while my graduate physics level used Jackson's electrodynamics text. Jackson's is pretty hard to penetrate but really, the two texts diverge on what they cover on the higher topics. Jackson is more interested in topics concerning physics like particles and relativity while Balanis focuses on stuff like general electromagnetic waves and their computation. Both of these are meant for higher levels and I think you should confine your initial inquiries to Griffiths.

 

[KhalDirth]

Perhaps you are familiar with the William Hayt book, "Engineering Electromagnetics"? It was the text used in my undergrad for the Intro to Electrodynamics course. Still, I will also look into purchasing the Griffiths.

 

[Born2bwire]

Actually I must admit an embarrassing ignorance of introductory texts. I have taken four physics courses on electromagnetics and many ECE courses on electromagnetics. But the only introductory text I ever used was Griffiths, the rest were lecture slides on the whole. I am much more familiar with the advanced level texts like Jackson, Balanis, Chew, Harrington, Stratton just to rattle off some names from the top of my head. I guess I have gotten to be a prime example of not being able to see the forest for the trees. Anyway, I have to sign off, too damn late out here.

I will note though that electromagnetic waves are usually not discussed in the first introductory electrodynamics course. They usually focus on the more basic manipulation of Maxwell's equations like dealing with Ampere's Law or Faraday's Law by themselves. The wave equations are reliant on all four of Maxwel's equations. So this is generally relegated to a second or third semester on electrodynamcs before it is introduced. But the discussion on electromagnetic wave theory never stops, it just keeps on going into higher levels so you will find a whole range of books of varying difficulties on the subject.

 

[KhalDirth]

Actually I must admit an embarrassing ignorance of introductory texts. I have taken four physics courses on electromagnetics and many ECE courses on electromagnetics. But the only introductory text I ever used was Griffiths, the rest were lecture slides on the whole. I am much more familiar with the advanced level texts like Jackson, Balanis, Chew, Harrington, Stratton just to rattle off some names from the top of my head. I guess I have gotten to be a prime example of not being able to see the forest for the trees. Anyway, I have to sign off, too damn late out here.

I will note though that electromagnetic waves are usually not discussed in the first introductory electrodynamics course. They usually focus on the more basic manipulation of Maxwell's equations like dealing with Ampere's Law or Faraday's Law by themselves. The wave equations are reliant on all four of Maxwel's equations. So this is generally relegated to a second or third semester on electrodynamcs before it is introduced. But the discussion on electromagnetic wave theory never stops, it just keeps on going into higher levels so you will find a whole range of books of varying difficulties on the subject.

Ah, perhaps this is why I am lacking in the wave department (only one semester on electromagnetics in undergrad during which, as you say, we manipulated the laws by themselves). Either way, thanks for the help.

 

[Bob S]

Oh yes. Pretty much the entirety of classical electrodynamics comes from just five equations. The four equations of Maxwell's equations and the Lorentz force which relates to force on a charge due to electric and magnetic fields. That's it, that's pretty much the entire basis of electromagnetics (with electrostatics being a subset of electromagnetics (or electrodynamics if you like)).

For most intents and purposes, it is not possible to have a longitudinal electromagnetic wave. In a source-free homogeneous region, you can only have transverse waves. The propagating waves are transverse waves. Now, exceptions can be made if we have in inhomogeneous region, a lot of surface waves are longitudinal. And confined waves can also be longitudinal, but often times it is a fake longitudinal... .

It is possible to put a microwave oscillator (magnetron or reflex klystron) on one end of a waveguide (S band or X band for example) and create a traveling TE or TM wave) in the waveguide with longitudinal components. An appropriately designed horn will match the TE or TM wave to free space (Z₀ = sqrt(μ₀/ε₀) = 377 ohms) and transmit a signal.

This is based on Maxwell's equations without use of the Lorentz force equation.
Bob S

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