Deriving Maxwell's Equations: Primitive Assumptions Explained

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    Maxwell's equations
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Discussion Overview

The discussion revolves around the derivation of Maxwell's equations, focusing on the primitive assumptions that could be used to explain them to a non-physics audience. Participants explore various approaches, historical contexts, and the foundational nature of these equations within classical electrodynamics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant requests resources for deriving Maxwell's equations starting from primitive assumptions for a presentation.
  • Another participant notes that Maxwell's equations are derived from experimental evidence rather than fundamental assumptions, citing Gauss's Law and Faraday's Law as examples.
  • A later reply mentions that the displacement current term in Ampere's Law was added by Maxwell for mathematical consistency.
  • One participant suggests looking at the American Journal of Physics for articles on pedagogical approaches to deriving Maxwell's equations.
  • Another participant argues that Maxwell's equations are fundamental and cannot be derived, although they mention a different approach starting from electrostatics and special relativity that leads to the invention of magnetism.

Areas of Agreement / Disagreement

Participants express differing views on whether Maxwell's equations can be derived or are fundamental. Some emphasize the experimental basis for the equations, while others suggest alternative approaches that may lead to their formulation.

Contextual Notes

Participants highlight the complexity of explaining these concepts to a lay audience and the potential limitations of various derivation approaches, including the need for assumptions and the historical context of the equations.

Who May Find This Useful

This discussion may be of interest to students and educators in physics, particularly those looking for pedagogical methods to explain Maxwell's equations and their derivation.

chaotixmonjuish
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Could someone point me in the direction of the derviation of each of Maxwell's equations? I'm working on a presentation and can't find a good one that starts with primitive assumptions (i.e. to help explain to a non physics audience).
 
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As far as I know, in classical electrodynamics, Maxwell's equations are ultimately "derived" from experimental evidence, not from more fundamental assumptions. Gauss's Law comes from studies of electric forces by Coulomb and others. Faraday's Law comes from experiments on magnetic induction, most notably by Faraday himself.

The one exception would be the part of Ampere's Law that was added by Maxwell in order to make the complete set of equations mathematically consistent (the "displacement current" term).

In modern quantum theory, one can derive electrodynamics (including Maxwell's equations) by requiring that the theory be invariant under local U(1) gauge transformations of the particle fields. See for example the last section of

http://www.upscale.utoronto.ca/GeneralInterest/DBailey/SubAtomic/Lectures/LectF13/Lect13.htm

I wouldn't want to try to explain this to a lay audience though. :bugeye:
 
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Try a search at Amer J Phys, which frequently focuses on pedagogical aspects and interesting derivations. There have been several articles on deriving Maxwell's equations over the years.
 
Maxwell's equations are usually considered the most fundamental equations of classical electromagnetism, and therefore cannot be derived. They are accepted because they successfully predict the widest range of classical electromagnetic phenomena. However, if you there is a slightly different approach where you can start with electrostatics, and assume special relativity, and then you are force to invent magnetism, or something like that. I don't remember the details, and I don't know how fudge free this approach is, but you can look at Ohanian's EM text for details.
 

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