SO: Why then, do we get a shock when we touch a wire carrying current, assuming we are grounded, and not get a shock passing through the fields generated by the current, if the energy is actually being carried by the fields? ALSO- these fields are generated without current aren't they- as in wireless technology? Thanks, great. piece, great comments.
That’s a good question. The fields can’t jump the gap unless there’s a conducting path. And it’s the flow of current that’s particularly harmful and causes shocks or death by electrocution.
I finally got around to reading this, and I really want to read all your work (when my hard time constraints permit). As a mech eng I never was properly taught the Maxwell equations, and am only now starting to understand them. I am REALLY glad you added the equation in this article P=VI=Surface Integral of E x H over the resistor, I never understand this before and it is a revelation. Can you confirm that this is the accepted way to understand energy flux, that is E x H? Like NO ONE in traditional electrical power engineering can normally explain this.....
Thanks for the kind words. There are some subtleties and ambiguities I didn't want to get into on a first pass through the subject. Not everyone agrees that it's just E x H. I'll be discussing the principal objections and my view of them in Chapter 8. I believe it is, and that belief has served me well developing the laws that govern near-field interactions for electrically-small antennas operating well within a wavelength or so of a source. Also, E x H is the basis for our understanding of antenna link laws which have successfully and accurately described antenna links to the moon and beyond (for instance the link to the Voyager space probes). More detail coming in Chapter 8.
In your article 4.1 I found it interesting the commentary about how current I being the carrier of charge, was the obvious thing to assume was also transmitting power, but I dont think this is correct. I finally understood how you determine the direction of AC power flow, in 2 power factor quadrants its one way, and in the other two, the other way, but I still dont think this explains WHY the power always flows in the same direction for a fixed phase angle. The only way that explained it for me was via the Poynting Vector, and that the E and H cross product is always in the same direction for a given phase angle even as the current alternates.
Heaviside did more to obscure than to develop EM theory. His formulation using vectors was simply wrong. The electric field and the magnetic field are of different dimensions, the former can be treated as a vector, but then the latter is a bivector, or oriented area. "Axial vectors" and cross-products are bunk. If W.K. Clifford hadn't died before his 34th birthday in 1879, EM theory and physics in general would have been advanced by decades. See John Denker's translation of Maxwell/Heaviside equations into Geometric/Clifford Algebra: https://www.av8n.com/physics/maxwell-ga.htm - many other worthwhile articles on his site.
Though the fluid analogy has limitations when dealing with fields, it is far better for understanding actual circuits than Heaviside's obscure thickets of notation. When I taught electronics to elementary school students, fluid theory was the only way to build their intuition, and it worked well for not only resistors and voltage sources, but Kirchoff's rules, capacitors, (at least the phase behavior of) inductors, and even BJTs and FETs. I often used (amasci.com) Bill Beatty's diagrams for the fluid analogy examples, but he also had a better illustration of the fields around a circuit the same as your example above, and his "duck disruptor" was a far more enlightening example of a phased-array emitter than anything in a textbook.
That's an interesting approach. Do you know if anyone has translated that approach into link laws for antennas so that it can be tested and compared to the conventional formulations?
I don't find papers or software directly using Geometric Algebra for ordinary antenna design, though there are some on antenna arrays. A search on Google Scholar for "Geometric Algebra" + "antenna design" gives a few results, J. Lasenby's papers are always good (The Cambridge Group geometry.mrao.cam.ac.uk has some of the best introductions to GA, esp. Chris Doran (top in GA physics, also introduced real-time lighting to games); "Slehar" has the best visual / conceptual web intro.; don't bother with Wikipedia). Searching on: ""Geometric Algebra" antenna design" Yandex had the best results, followed by DuckDuckGo. Peeter Joot's "Geometric Algebra for Electrical Engineers" may be useful, but I haven't read it. He put out a fine open work on physics, where he worked through many problems, a vast amount of work.
"I like work; it fascinates me. I can sit and look at it for hours." - Jerome K. Jerome
Joot's 200+ page course notes on antenna theory have a few references to GA equivalent formulations, but it's well below your level.
What I have found is using GA in transformers and generative design tools, e.g. I've been a fan of Taco Cohen's Geometric Algebra Transformer ("GATr", ML/AI) approach for a while now, he's at Qualcomm, but I didn't see it used for antennas. There's a Github repo, but it will be some effort to apply. I prefer conformal GA (+2D), which can handle spheres; GATr uses the +1D projective GA, which is more computationally efficient, but can handle only planes. A variant, called Wi-GATr ( https://arxiv.org/abs/2406.14995 ) is being used for wireless signal propagation modelling, but the paper has nothing on antenna design.
Zhi Ning Chen of National University of Singapore is giving a plenary lecture Sept. 2 at the ICEAA-IEEE APWC conference: "Antenna+AI: Generative Antenna Design Reshapes Metantenna Technology", but it is unclear if he's using GA and his topic seems to be primarily metalenses.
Isn't amazing how electrodynamics can be explained through fluid mechanics. Electricity is able to adapt just like water can to its surroundings. These relationships are proof that energy is a form of energetic fluid of some sort.
Is the necessity for a medium through which energy may flow (be transmitted from place to place) the core reason for the theories about gravitons, for example? The reality that gravity appears to propagate in free space (vacuum, nothing), plus the proposition that energy must have a medium by which to propagate, and the desire to avoid re-litigating all that tedious argument about the ether, leads inevitably to particle theories of gravity and other fields?
I started looking at gravitational energy and my advisor wisely told me to look at electromagnetic theory instead. There are any number of intriguing problems with gravitational fields, including the fact that they may propagate faster than light. I'll stick to trying to understand electromagnetism, because I think that's a more tractable problem.
I really enjoy reading your publications. I am a simulation expert for electromagnetic fields and all of the history in your posts was very interesting and new to me.
In todays post, where you discuss the transfer of Energy by Poyntings theorem I noticed that you relay on analytical solutions which involve a lot of complex vector analysis. As a simulation guy I did many of these experiments using full wave simulation tools and I think that interactive plots of electromagnetic fields can help a lot in understanding the behaviour of fields. You can check my take on Poynting in this video:
SO: Why then, do we get a shock when we touch a wire carrying current, assuming we are grounded, and not get a shock passing through the fields generated by the current, if the energy is actually being carried by the fields? ALSO- these fields are generated without current aren't they- as in wireless technology? Thanks, great. piece, great comments.
That’s a good question. The fields can’t jump the gap unless there’s a conducting path. And it’s the flow of current that’s particularly harmful and causes shocks or death by electrocution.
But we are told the current doesn’t ‘flow’! Wild!
I finally got around to reading this, and I really want to read all your work (when my hard time constraints permit). As a mech eng I never was properly taught the Maxwell equations, and am only now starting to understand them. I am REALLY glad you added the equation in this article P=VI=Surface Integral of E x H over the resistor, I never understand this before and it is a revelation. Can you confirm that this is the accepted way to understand energy flux, that is E x H? Like NO ONE in traditional electrical power engineering can normally explain this.....
Thanks for the kind words. There are some subtleties and ambiguities I didn't want to get into on a first pass through the subject. Not everyone agrees that it's just E x H. I'll be discussing the principal objections and my view of them in Chapter 8. I believe it is, and that belief has served me well developing the laws that govern near-field interactions for electrically-small antennas operating well within a wavelength or so of a source. Also, E x H is the basis for our understanding of antenna link laws which have successfully and accurately described antenna links to the moon and beyond (for instance the link to the Voyager space probes). More detail coming in Chapter 8.
In your article 4.1 I found it interesting the commentary about how current I being the carrier of charge, was the obvious thing to assume was also transmitting power, but I dont think this is correct. I finally understood how you determine the direction of AC power flow, in 2 power factor quadrants its one way, and in the other two, the other way, but I still dont think this explains WHY the power always flows in the same direction for a fixed phase angle. The only way that explained it for me was via the Poynting Vector, and that the E and H cross product is always in the same direction for a given phase angle even as the current alternates.
Also, this little program called a teaching toy I found really good to explain AC power basics: http://mail.pqube3.com/PQTeachingToyIndex.php
Thanks, this video is what turned me on to the Poynting Vector as explaining energy flux: https://www.youtube.com/watch?v=bHIhgxav9LY
Heaviside did more to obscure than to develop EM theory. His formulation using vectors was simply wrong. The electric field and the magnetic field are of different dimensions, the former can be treated as a vector, but then the latter is a bivector, or oriented area. "Axial vectors" and cross-products are bunk. If W.K. Clifford hadn't died before his 34th birthday in 1879, EM theory and physics in general would have been advanced by decades. See John Denker's translation of Maxwell/Heaviside equations into Geometric/Clifford Algebra: https://www.av8n.com/physics/maxwell-ga.htm - many other worthwhile articles on his site.
Though the fluid analogy has limitations when dealing with fields, it is far better for understanding actual circuits than Heaviside's obscure thickets of notation. When I taught electronics to elementary school students, fluid theory was the only way to build their intuition, and it worked well for not only resistors and voltage sources, but Kirchoff's rules, capacitors, (at least the phase behavior of) inductors, and even BJTs and FETs. I often used (amasci.com) Bill Beatty's diagrams for the fluid analogy examples, but he also had a better illustration of the fields around a circuit the same as your example above, and his "duck disruptor" was a far more enlightening example of a phased-array emitter than anything in a textbook.
That's an interesting approach. Do you know if anyone has translated that approach into link laws for antennas so that it can be tested and compared to the conventional formulations?
I don't find papers or software directly using Geometric Algebra for ordinary antenna design, though there are some on antenna arrays. A search on Google Scholar for "Geometric Algebra" + "antenna design" gives a few results, J. Lasenby's papers are always good (The Cambridge Group geometry.mrao.cam.ac.uk has some of the best introductions to GA, esp. Chris Doran (top in GA physics, also introduced real-time lighting to games); "Slehar" has the best visual / conceptual web intro.; don't bother with Wikipedia). Searching on: ""Geometric Algebra" antenna design" Yandex had the best results, followed by DuckDuckGo. Peeter Joot's "Geometric Algebra for Electrical Engineers" may be useful, but I haven't read it. He put out a fine open work on physics, where he worked through many problems, a vast amount of work.
"I like work; it fascinates me. I can sit and look at it for hours." - Jerome K. Jerome
Joot's 200+ page course notes on antenna theory have a few references to GA equivalent formulations, but it's well below your level.
What I have found is using GA in transformers and generative design tools, e.g. I've been a fan of Taco Cohen's Geometric Algebra Transformer ("GATr", ML/AI) approach for a while now, he's at Qualcomm, but I didn't see it used for antennas. There's a Github repo, but it will be some effort to apply. I prefer conformal GA (+2D), which can handle spheres; GATr uses the +1D projective GA, which is more computationally efficient, but can handle only planes. A variant, called Wi-GATr ( https://arxiv.org/abs/2406.14995 ) is being used for wireless signal propagation modelling, but the paper has nothing on antenna design.
Zhi Ning Chen of National University of Singapore is giving a plenary lecture Sept. 2 at the ICEAA-IEEE APWC conference: "Antenna+AI: Generative Antenna Design Reshapes Metantenna Technology", but it is unclear if he's using GA and his topic seems to be primarily metalenses.
A fascinating recounting, even if EM field maps drawn over circuits still give me cold sweats.
Isn't amazing how electrodynamics can be explained through fluid mechanics. Electricity is able to adapt just like water can to its surroundings. These relationships are proof that energy is a form of energetic fluid of some sort.
Silvanus P. Thompson was translator into English of both William Gilbert's De Magnete and Cristiaan Huygens's Traité de la Lumière.
Is the necessity for a medium through which energy may flow (be transmitted from place to place) the core reason for the theories about gravitons, for example? The reality that gravity appears to propagate in free space (vacuum, nothing), plus the proposition that energy must have a medium by which to propagate, and the desire to avoid re-litigating all that tedious argument about the ether, leads inevitably to particle theories of gravity and other fields?
I started looking at gravitational energy and my advisor wisely told me to look at electromagnetic theory instead. There are any number of intriguing problems with gravitational fields, including the fact that they may propagate faster than light. I'll stick to trying to understand electromagnetism, because I think that's a more tractable problem.
Hello Hans,
I really enjoy reading your publications. I am a simulation expert for electromagnetic fields and all of the history in your posts was very interesting and new to me.
In todays post, where you discuss the transfer of Energy by Poyntings theorem I noticed that you relay on analytical solutions which involve a lot of complex vector analysis. As a simulation guy I did many of these experiments using full wave simulation tools and I think that interactive plots of electromagnetic fields can help a lot in understanding the behaviour of fields. You can check my take on Poynting in this video:
https://www.youtube.com/watch?v=09DnbKq240s
Let me know if you have interest in some simulation results to be included in your publication.
BR
Andreas
Excellent video. I'll be in touch.
I will take a look at your video and get back to you.