Deriving the curl of the magnetic field

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SUMMARY

The discussion centers on the derivation of the curl of the magnetic field, specifically the equations c²∇×B = j/ε₀ and ∇×B = μ₀j. Participants reference Feynman's lectures for foundational concepts and inquire about the mathematical transition between integrals using Stokes' theorem. The Biot-Savart law is also mentioned as a critical component in understanding the curl of magnetic fields. This highlights the importance of both theoretical and mathematical frameworks in electromagnetism.

PREREQUISITES
  • Understanding of Maxwell's equations
  • Familiarity with vector calculus, specifically Stokes' theorem
  • Knowledge of the Biot-Savart law
  • Basic concepts of electromagnetism
NEXT STEPS
  • Study the derivation of Maxwell's equations in detail
  • Learn about Stokes' theorem and its applications in electromagnetism
  • Explore the Biot-Savart law and its implications for magnetic fields
  • Investigate the mathematical techniques for transitioning between different integral forms
USEFUL FOR

Physics students, electrical engineers, and anyone interested in advanced electromagnetism and vector calculus applications.

pkjag
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So i was wondering how the curl of the magnetic field is derived since Feynman just introduces it from nothing in his second volume of Feynman's lectures on physics:

c2xB=j0

or the other one where ∇x B=μ0j
 
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Do you know about the Biot-Savart's law and how to pass mathematically from one type of integral to another (Stokes formulas) ?
 

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