Determining c from Maxwell's Equations

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    Maxwell's equations
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Discussion Overview

The discussion centers around the determination of the speed of light (c) from Maxwell's equations, exploring the relationships between electric and magnetic fields in electromagnetic waves. Participants seek to understand how c can be derived conceptually and mathematically from these equations, as well as the historical context of measuring the speed of light prior to Maxwell's work.

Discussion Character

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

Main Points Raised

  • One participant expresses confusion about how velocity can be calculated from the relationships between electric and magnetic fields in electromagnetic waves, seeking a non-mathematical explanation.
  • Another participant suggests that the speed of a wave is determined by the resistance to displacement and the response to restoring forces, drawing parallels to electromagnetic radiation.
  • There is a discussion about the presence of c in Maxwell's equations and whether it was known prior to their formulation, with some participants questioning how c was logically arrived at without using math.
  • Participants note that the speed of light was measured before Maxwell's equations were established, with historical references to early measurements by Newton and others.
  • One participant clarifies that c and the speed of light are not the same concept, prompting further questions about whether Maxwell's equations allow for the determination of c or merely show that light travels at that speed.
  • Another participant explains that Maxwell derived the relationship c = 1 / √(μ₀ε₀) from his equations, using previously measured values of μ₀ and ε₀.
  • There is a question about whether the equation for c was formulated to match the measured speed of light or if it was derived independently of that measurement.
  • One participant highlights the significance of deriving c from Maxwell's equations, suggesting that it implies a prior understanding of a constant related to the speed of light.
  • A later post introduces the differential wave equation and its relation to Maxwell's equations, indicating that solutions to these equations also yield the same form as the wave equation.

Areas of Agreement / Disagreement

Participants express various viewpoints regarding the relationship between c, the speed of light, and Maxwell's equations. There is no consensus on whether c was derived to match the speed of light or if it was an independent constant recognized in the context of electromagnetic theory.

Contextual Notes

Participants reference historical measurements of the speed of light and the development of electromagnetic theory, indicating a complex interplay between empirical observations and theoretical formulations. There are unresolved questions about the nature of c and its derivation from Maxwell's equations.

  • #31
bryanso said:
Hi, I hope someone can explain this mystery to me. When we set j to zero, why doesn't the displacement current term also vanish? There is no charge, no current, hence no E field, right?
The displacement current is no current. Its name is from a highly complicated and utterly wrong early mechanical model invented by Maxwell to "derive" is famous equations. Maxwell himself later abandoned all these mechanical models and came to the conclusion that the electromagnetic field is a fundamental entity with no need for any mechanical models.
 
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  • #32
vanhees71, Thank you very much. This is the most intuitive explanation. I will reread displacement current with this history perspective in mind.
 

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