History of Maxwell's Equations #1: Gauss's Law
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Date: 2022-12-27
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Comments and reviews: 20
Alan
Kathy presents an excellent lecture. I enjoyed it very much. I have studied electromagnetism in various forms for my entire professional career. I would just add two comments to Kathy's presentation. First, the (mature) men in the 19th century almost always have beards and bushy sideburns, because the safety razor would not be invented and sold by King Gillette until 1904. A man trying to shave in the 19th century would use a straight razor and it was extremely difficult to do this every day without a skilled and trusted barber or servant, if you wanted to avoid cuts on your face. This is why Maxwell, Faraday, and Heaviside are all shown with beards. The invention of the safety razor changed that, so that mature men in the 20th century are often clean shaven. The presence or absence of a beard on an adult man can indicate if he was in the 19th or 20th century. Second, the developments of electromagnetism did not stop with Maxwell's equations. There were further developments and refinements with unification with Einsteinian Relativity and Quantum Mechanics in the 20th century, and even further development in the 21st century with the application of Geometric Algebra ideas from David Hestenes and others. Heaviside's formulations of Maxwell's equations are quite useful, but they were constructed before the implications of relativity and quantum mechanics were understood. Geometric Algebra is one mathematical idea for further unification and extension.
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Kathy presents an excellent lecture. I enjoyed it very much. I have studied electromagnetism in various forms for my entire professional career. I would just add two comments to Kathy's presentation. First, the (mature) men in the 19th century almost always have beards and bushy sideburns, because the safety razor would not be invented and sold by King Gillette until 1904. A man trying to shave in the 19th century would use a straight razor and it was extremely difficult to do this every day without a skilled and trusted barber or servant, if you wanted to avoid cuts on your face. This is why Maxwell, Faraday, and Heaviside are all shown with beards. The invention of the safety razor changed that, so that mature men in the 20th century are often clean shaven. The presence or absence of a beard on an adult man can indicate if he was in the 19th or 20th century. Second, the developments of electromagnetism did not stop with Maxwell's equations. There were further developments and refinements with unification with Einsteinian Relativity and Quantum Mechanics in the 20th century, and even further development in the 21st century with the application of Geometric Algebra ideas from David Hestenes and others. Heaviside's formulations of Maxwell's equations are quite useful, but they were constructed before the implications of relativity and quantum mechanics were understood. Geometric Algebra is one mathematical idea for further unification and extension.
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David
Heaviside is the only reason we understand Maxwell now - before Heaviside, there were 20-21 equations with as many unknowns. Heaviside reformulated these into the 4 recognized equations we use today.
Heaviside was treated very unfairly, and from my recollection, this was due to his Operational Calculus. His response to their accusation that he didn't prove, mathematically rigorously, that this method worked, was along the lines of: Just because I don't know understand how my body digests my breakfast, doesn't mean I shouldn't eat it. BTW - it works. His efforts, along with Charles Proteus Steinmetz (almost not allowed into the USA b/c of his dwarfism, are the sole reason electricity is engineerable.
Heaviside eventually go so fed up with the criticism from the British establishment, that he stopped writing. He did something like painted his fingernails and removed all the furniture from his house, and gave up.
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Heaviside is the only reason we understand Maxwell now - before Heaviside, there were 20-21 equations with as many unknowns. Heaviside reformulated these into the 4 recognized equations we use today.
Heaviside was treated very unfairly, and from my recollection, this was due to his Operational Calculus. His response to their accusation that he didn't prove, mathematically rigorously, that this method worked, was along the lines of: Just because I don't know understand how my body digests my breakfast, doesn't mean I shouldn't eat it. BTW - it works. His efforts, along with Charles Proteus Steinmetz (almost not allowed into the USA b/c of his dwarfism, are the sole reason electricity is engineerable.
Heaviside eventually go so fed up with the criticism from the British establishment, that he stopped writing. He did something like painted his fingernails and removed all the furniture from his house, and gave up.
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Swami
- ANOTHER FANTASTIC VIDEO - as always: )
- Having a formal education in electrical engineering, and being a self-taught math teacher (by nature/profession, and a lover of history, your subject matter, and presentation are richly appreciated.
- Now, as for quaternions, I've also been a 3D animator, where me initial exposure to quaternions arose (for rotations. And, I've heard that Maxwell's Equations were originally written in the form of quaternions - so, I was excited to get the details of exactly why/how. only to find I will have to wait for your next heroic effort! So, I await in giddy antici. pation: ).
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- ANOTHER FANTASTIC VIDEO - as always: )
- Having a formal education in electrical engineering, and being a self-taught math teacher (by nature/profession, and a lover of history, your subject matter, and presentation are richly appreciated.
- Now, as for quaternions, I've also been a 3D animator, where me initial exposure to quaternions arose (for rotations. And, I've heard that Maxwell's Equations were originally written in the form of quaternions - so, I was excited to get the details of exactly why/how. only to find I will have to wait for your next heroic effort! So, I await in giddy antici. pation: ).
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ter
This is another great Kathy Loves Physics video. After watching it, I did an internet and Web of Science search trying to find out why Gauss's law is named after Gauss. I think the video at about 21: 25 alludes to Maxwell applying the divergence theorem, which is credited to Gauss, perhaps among others. If Faraday is credited with proposing what are now called field lines, Maxwell described what we now call Gauss's law in both integral and differential form and Heaviside re-cast Maxwell's equations in the language of vector calculus, what did Gauss do?
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This is another great Kathy Loves Physics video. After watching it, I did an internet and Web of Science search trying to find out why Gauss's law is named after Gauss. I think the video at about 21: 25 alludes to Maxwell applying the divergence theorem, which is credited to Gauss, perhaps among others. If Faraday is credited with proposing what are now called field lines, Maxwell described what we now call Gauss's law in both integral and differential form and Heaviside re-cast Maxwell's equations in the language of vector calculus, what did Gauss do?
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titicoqui
the rarest of pleasures this I absolutely love the story of maxwell-faraday's companionship makes me weepy. not only listen to her words but follow the continuous sparkle in her eyes as she is fully grasping something we seem to understand only in parts. maxwell died from the same stomach cancer that killed his mother at the same age 47 i am less than an amateur on the subject of physics but maxwell remains for me number 3 in sheer intellectual prowess and magnitude after newton and einstein.
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the rarest of pleasures this I absolutely love the story of maxwell-faraday's companionship makes me weepy. not only listen to her words but follow the continuous sparkle in her eyes as she is fully grasping something we seem to understand only in parts. maxwell died from the same stomach cancer that killed his mother at the same age 47 i am less than an amateur on the subject of physics but maxwell remains for me number 3 in sheer intellectual prowess and magnitude after newton and einstein.
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Muli
This is a great exposition of Coulomb's, Faraday, and Maxwell enormous achievements. Thank you. It must be noted, however, the Feynman's dismissal of the Civil war as side note compared to this, i. e, the war against one of the greatest systematic crime's against humanity (slavery), is infantile. Indeed, there are many signs that outside his field, Feynman was thinking as an infantile, and let us take heed of not to over glorify geniuses beyond their actual (enormous) contributions.
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This is a great exposition of Coulomb's, Faraday, and Maxwell enormous achievements. Thank you. It must be noted, however, the Feynman's dismissal of the Civil war as side note compared to this, i. e, the war against one of the greatest systematic crime's against humanity (slavery), is infantile. Indeed, there are many signs that outside his field, Feynman was thinking as an infantile, and let us take heed of not to over glorify geniuses beyond their actual (enormous) contributions.
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Louis
My grandmother was born in 1868. Just three years after the American Civil War. The war that Fiineman thought was insignificant compared to Maxwells equations. That hasnt been all that long ago. Look at what has been discovered. My mother, her youngest daughter, told me she was offered a scholarship to the University of Arkansas. That just didnt happen to women back then. Her father refused it. He didnt think women needed an education. A lot has changed since then.
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My grandmother was born in 1868. Just three years after the American Civil War. The war that Fiineman thought was insignificant compared to Maxwells equations. That hasnt been all that long ago. Look at what has been discovered. My mother, her youngest daughter, told me she was offered a scholarship to the University of Arkansas. That just didnt happen to women back then. Her father refused it. He didnt think women needed an education. A lot has changed since then.
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neail
It is an absolute necessity to go through the history to understand the development, if included in syllabus it will really put colours in the repulsive textbooks, we all have gone through hours of memorization before truly convincing ourselves through understanding, that process might be more forgiving and seeing the leaders of the fields to fumble and try and fail might give courage.
Another masterpiece, thank you.
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It is an absolute necessity to go through the history to understand the development, if included in syllabus it will really put colours in the repulsive textbooks, we all have gone through hours of memorization before truly convincing ourselves through understanding, that process might be more forgiving and seeing the leaders of the fields to fumble and try and fail might give courage.
Another masterpiece, thank you.
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Wardell
Maxwell's Law Corrected!
Copyright 2022 Wardell Lindsay
Quaternion Derivative X=[d/dr, Del]
Quaternion B=[-scalar b, Vector B]
0=XB=[d/dr, Del] [-b, B]
0=[db/dr - Del. B,
dB/dr - Del b + DelxB]
0=[db/dr - db/dr CosB,
-dB/dr + dB/dr + DelxB SinB]
0=XB=[db/dr - db/dr CosB,
db/dr HSinB]
0=XB=db/dr[1- CosB, HSinB]
0=XB=ro [1 - CosB, HSinB]
This the Correct Maxwell's Equation.
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Maxwell's Law Corrected!
Copyright 2022 Wardell Lindsay
Quaternion Derivative X=[d/dr, Del]
Quaternion B=[-scalar b, Vector B]
0=XB=[d/dr, Del] [-b, B]
0=[db/dr - Del. B,
dB/dr - Del b + DelxB]
0=[db/dr - db/dr CosB,
-dB/dr + dB/dr + DelxB SinB]
0=XB=[db/dr - db/dr CosB,
db/dr HSinB]
0=XB=db/dr[1- CosB, HSinB]
0=XB=ro [1 - CosB, HSinB]
This the Correct Maxwell's Equation.
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Marc
Very interesting video! Just a nitpick about the term dielectric (11: 52): the cited page by Faraday does not mention the number 2 in any explicit or implicit form, but he does say substance through or across which electric forces are acting. That suggests the etymology dia-electric (from dia through) rather then di-electric. Indeed a rapid online search suggests that dia is the right origin.
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Very interesting video! Just a nitpick about the term dielectric (11: 52): the cited page by Faraday does not mention the number 2 in any explicit or implicit form, but he does say substance through or across which electric forces are acting. That suggests the etymology dia-electric (from dia through) rather then di-electric. Indeed a rapid online search suggests that dia is the right origin.
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Mark
Wow! I am so loving this. When I was studying Electronics back in the 80s I could structure my understanding of the theory by putting it in the context of the historical emergence of said knowledge. It gave me a structure to weave the theory around. A filing system if you will. BTW I can hear the influence of Feynman in your voice and presentation. You are clearly an admirer of his as am I.
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Wow! I am so loving this. When I was studying Electronics back in the 80s I could structure my understanding of the theory by putting it in the context of the historical emergence of said knowledge. It gave me a structure to weave the theory around. A filing system if you will. BTW I can hear the influence of Feynman in your voice and presentation. You are clearly an admirer of his as am I.
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Paul
Faraday is an absolute hero of mine!
If you ever come to London, UK, you really must visit the Royal Institution and attend a Friday evening lecture in the very room he himself lectured in, amongst very many subsequent greats. Truly evidence of the shoulders of giants in that one small auditorium.
Given your love of the history of science, I know youll love and never forget it!
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Faraday is an absolute hero of mine!
If you ever come to London, UK, you really must visit the Royal Institution and attend a Friday evening lecture in the very room he himself lectured in, amongst very many subsequent greats. Truly evidence of the shoulders of giants in that one small auditorium.
Given your love of the history of science, I know youll love and never forget it!
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John
Thank you Kathy for another wonderful video. As an EE grad (1981) we were taught Maxwell's equations. But digging in, and understanding them deeply were graduate courses. Your videos have brought me a much deeper understanding of them. It's great to see how they grew and changed over time and its much easier to see what they mean when seen from this historical context.
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Thank you Kathy for another wonderful video. As an EE grad (1981) we were taught Maxwell's equations. But digging in, and understanding them deeply were graduate courses. Your videos have brought me a much deeper understanding of them. It's great to see how they grew and changed over time and its much easier to see what they mean when seen from this historical context.
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Rice
Great video! I hope in this series you will discuss Irish mathematician James MacCullagh's interpretation of the electromagnetic equations in 1839 and if Heaviside new of this work. And speaking of obscure Irish, it would be great to see a video on Edward Hutchison Synge who invented near-field optical microscopy, piezoelectric scanning, and LIDAR. Cheers.
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Great video! I hope in this series you will discuss Irish mathematician James MacCullagh's interpretation of the electromagnetic equations in 1839 and if Heaviside new of this work. And speaking of obscure Irish, it would be great to see a video on Edward Hutchison Synge who invented near-field optical microscopy, piezoelectric scanning, and LIDAR. Cheers.
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John
at 22: 46 we have multiply both sides by k. Works fine on the right hand side, but notice that on the left k is slyly put to the right of the derivative operator. This is fine as along as k is spatially constant, but it doesn't work if k is inhomogeneous.
That's why Electrical Engineers write del dot D = rho rather than del dot E = rho/epsilon.
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at 22: 46 we have multiply both sides by k. Works fine on the right hand side, but notice that on the left k is slyly put to the right of the derivative operator. This is fine as along as k is spatially constant, but it doesn't work if k is inhomogeneous.
That's why Electrical Engineers write del dot D = rho rather than del dot E = rho/epsilon.
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Karol
100% nothing = 0% something, 100% something = 0% nothing. these value are limits! what likely exist? penultimate of 100% nothing and penultimate of 100% something
penultimate of 100% something, always reify penultimate of 100% nothing! penultimate of 100% nothing can not reify penultimate of 100% something! logic 101 for beginner
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100% nothing = 0% something, 100% something = 0% nothing. these value are limits! what likely exist? penultimate of 100% nothing and penultimate of 100% something
penultimate of 100% something, always reify penultimate of 100% nothing! penultimate of 100% nothing can not reify penultimate of 100% something! logic 101 for beginner
reply
Aquarius
Kathy, Great Videos! Humanity really is in a Superman situation. Scientists, physicists, engineers need to figure this out ASAP and efficiently get our butts off this planet before our Sun vaporizes us all when it explodes and ends all life as we know it in this part of the universe. I have concepts that require your expertise.
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Kathy, Great Videos! Humanity really is in a Superman situation. Scientists, physicists, engineers need to figure this out ASAP and efficiently get our butts off this planet before our Sun vaporizes us all when it explodes and ends all life as we know it in this part of the universe. I have concepts that require your expertise.
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RDM
This woman is a total unicorn.
She understands history, she understands mathematics, she understands the science, she reveals the true scientific process, and shes able to teach it.
you dont need many people like this to absolutely change the world and my God shes doing it basically for free
Thank you.
Incredible.
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This woman is a total unicorn.
She understands history, she understands mathematics, she understands the science, she reveals the true scientific process, and shes able to teach it.
you dont need many people like this to absolutely change the world and my God shes doing it basically for free
Thank you.
Incredible.
reply
hbroadrider
If you havent seen it already, please read Oliver Heaviside: Sage in Solitude by Dr. Paul J. Nahin. It is a wonderful historical account of Heaviside. I was fortunate to be able to take classes from Dr. Nahin when I was in undergraduate engineering at UNH. Hes a fantastic story teller and gifted author
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If you havent seen it already, please read Oliver Heaviside: Sage in Solitude by Dr. Paul J. Nahin. It is a wonderful historical account of Heaviside. I was fortunate to be able to take classes from Dr. Nahin when I was in undergraduate engineering at UNH. Hes a fantastic story teller and gifted author
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tres
i am an idiot, but can anyone explain why PI is all over the place. I can understand 4Pi as the basis for calculating the surface of a sphere, but? Everything, from the surface/circumference of a circle, volume of a sphere, Maxwell's equations, Einstein's SR and GR relate to Pi. Why?
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i am an idiot, but can anyone explain why PI is all over the place. I can understand 4Pi as the basis for calculating the surface of a sphere, but? Everything, from the surface/circumference of a circle, volume of a sphere, Maxwell's equations, Einstein's SR and GR relate to Pi. Why?
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