Deriving the curl of the magnetic field

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The discussion focuses on the derivation of the curl of the magnetic field, specifically the equations c2∇xB=j/ε0 and ∇x B=μ0j. Participants express confusion over Feynman's introduction of these concepts without detailed derivation. The Biot-Savart law is mentioned as a crucial element in understanding the relationship between current and magnetic fields. Additionally, the mathematical transition between integral forms using Stokes' theorem is highlighted as a key aspect of the discussion. Understanding these principles is essential for grasping the underlying physics of magnetic fields.
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:

c2∇xB=j/ε0

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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