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Old Aug 11th 2014, 04:15 PM   #1
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maxwell equations

Hi
I'm studying maxwell's equations. I need historical references for Maxwell equations. I've read Maxwell articles and Heaviside articles and But I need a much deeper references.
What were the changes of these equations in history? Where these equations have been come?
Can you help me?
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Old Aug 12th 2014, 09:48 AM   #2
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You can start by looking into the history of each of the four equations:

1. Gauss's law for electric fields
2. Gauss's law for magnetic fields
3. Faraday's law
4. Ampere-Maxwell law

If you're interested in a good discussion of these equations and how Maxwell combined them to develop a comprehensive theory of electromagnetism, I suggest "A Student's Guide Maxwell's Equations" by Daniel Fleisch.
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Old Aug 12th 2014, 09:24 PM   #3
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I thought this was very interesting:

Maxwell's Equations on Youtube

What I found interesting was how Maxwell modified this equation:



to account for electromagnetic waves in a vacuum (without a current carrying conductor)



by taking a leaf out of Faraday's book. Interesting.
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Old Aug 13th 2014, 07:20 AM   #4
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Your question is more intriguing than most people realize. Because these equations have been altered a lot from the way they were originally conceived by Maxwell - due to the efforts of Heaviside, Fitzgerald, Lodge and Hertz. In brief:
  • There were initially twenty equations, later reduced by Heaviside to the four nowadays known as the Maxwell equations.
  • Faraday's electrotonic state, also called A field and vector potential, was originally understood to be a physical entity but was later regarded as a mere mathematical convenience by Heaviside. - However, a variety of phenomena known in modern physics, such as the Aharonov-Bohm and Altshuler-Aronov-Spivac effects, the Berry-Aharonov-Anandan phase, the Josephson effect, the quantum Hall effect, the De Haas-Van Alphen effect and the Sagnac effect show the vector potential to indeed be real.
  • The equations were originally written in quaternionic algebra, not vector calculus. This was seen as an unnecessary complexity by the Maxwell's successors mostly because quaternions are tricky to calculate with (especially without having computers). However, covering aforesaid effects in fact calls for usage of such a system of higher order symmetry forms.
You can read the whole story in much more detail in Terrence W. Barrett: Topological Foundations of Electromagnetism.

Hope this helps.

-Michael

Last edited by Curious; Aug 13th 2014 at 01:44 PM.
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Old Aug 13th 2014, 08:26 AM   #5
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TNX
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