Unraveling Faraday's Law: Formal Proof & Understanding the Transformation | Wiki

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SUMMARY

This discussion focuses on the formal proof of Faraday's Law of Induction and the transformation between its mathematical representations. The proof involves applying the chain rule while keeping one variable constant during differentiation, leading to an expression for the rate of change of magnetic flux. Additionally, the conversation highlights the relationship between Maxwell's equations and Faraday's Law, emphasizing the derivation of the electromotive force (emf) from the rate of change of magnetic flux. The linked Wikipedia page serves as a primary resource for understanding these concepts.

PREREQUISITES
  • Understanding of Faraday's Law of Induction
  • Familiarity with Maxwell's equations
  • Knowledge of calculus, specifically the chain rule
  • Basic concepts of electromagnetic fields
NEXT STEPS
  • Study the derivation of Faraday's Law from Maxwell's equations
  • Learn about the chain rule in calculus and its applications in physics
  • Explore the relationship between magnetic flux and electromotive force (emf)
  • Investigate advanced topics in electromagnetic theory, such as Lenz's Law
USEFUL FOR

Students of physics, electrical engineers, and educators seeking a deeper understanding of electromagnetic induction and its mathematical foundations.

LiftHeavy13
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Hi, I'm looking for a proof of faraday's law. This is the only page which gives a formal proof of it, but I do not understand the transformation from the first to the second step. It someone could help me out, I would appreciate it. Also, if someone could explain the opposite as well: how do you go from maxwell and faraday's differential equation to the actual equation for emf?

http://en.wikipedia.org/wiki/Faraday's_law_of_induction#Proof_of_Faraday.27s_law

sorry, i posted this in the calculus forum as well. was not sure which to put it in. thanks
 
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The first step is the chain rule so one variable is kept constant while another gets differentiated and vice versa and the two are summed together. Since the surface the integral is integrating over can vary with time, the surface is kept constant and the magnetic field is differentiated to get the first term and then the second term is obtained by differentiating the integral where the surface can vary with time but where the the magnetic field inside the integrand is kept constant.

The proof you linked pretty much does that already. It assumes one of the Maxwell's laws and derives an expression for the rate of change of flux. If you wanted to derive the formula for emf you would then proceed to assume Faraday's law for emf and substitute the derived formula for the rate of change of magnetic flux into it to get the formula for emf. The proof you linked does it the over way around so it assumes the law for emf first and substitues it into get Faraday's law.
 

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