I Determining c from Maxwell's Equations

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    Maxwell's equations
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The discussion centers on understanding how the speed of light (c) is derived from Maxwell's equations without delving into complex mathematics. Participants explain that the speed of electromagnetic waves is determined by the relationship between electric and magnetic fields, leading to a wave equation similar to those found in other physical contexts. It is clarified that c was measured before Maxwell's equations were formulated, and that Maxwell's equations incorporate the constants for permeability (μ) and permittivity (ε) to predict wave speed. The conversation emphasizes that Maxwell's discovery was a significant unification of light and electromagnetism, revealing that light behaves as an electromagnetic wave. Overall, the insights shared help clarify the logical connections between these fundamental concepts in physics.
  • #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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