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

In summary, the conversation discusses the proof of Faraday's law of induction, specifically the transformation from the first to the second step. The proof involves using the chain rule and differentiating the magnetic field while keeping the surface of integration constant. The source also discusses how the proof can be used to derive the equation for electromotive force (emf) by assuming one of the Maxwell's laws and substituting the derived formula for the rate of change of magnetic flux.
  • #1
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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  • #2
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.
 

1. What is Faraday's Law and why is it important in science?

Faraday's Law is a fundamental principle in electromagnetism that describes the relationship between a changing magnetic field and an induced electric field. It is important in science because it explains the concept of electromagnetic induction, which is the basis for many modern technologies such as generators, motors, and transformers.

2. How was Faraday's Law originally discovered?

Faraday's Law was discovered by British scientist Michael Faraday in the 1830s through a series of experiments involving magnets, electric coils, and motion. He noticed that when a magnet was moved near a conductor, an electric current was induced in the conductor, leading to his formulation of the law.

3. What is the formal proof for Faraday's Law?

The formal proof for Faraday's Law involves using mathematical equations to describe the relationship between the changing magnetic field (dB/dt) and the induced electric field (E) in a conductor. This can be expressed as E = -dB/dt, where the negative sign indicates that the induced electric field is in the opposite direction of the changing magnetic field.

4. How can one understand the transformation described by Faraday's Law?

One way to understand the transformation described by Faraday's Law is to visualize it using the concept of magnetic flux. Magnetic flux is a measure of the amount of magnetic field passing through a given area. When the magnetic flux changes, it induces an electric field, which can then produce an electric current in a conductor.

5. How is Faraday's Law applied in real-world applications?

Faraday's Law is applied in many real-world applications, such as generators, transformers, and motors. In generators, the rotation of a coil in a magnetic field induces an electric current, creating electricity. In transformers, Faraday's Law is used to convert high-voltage electricity to low-voltage electricity for safe use in homes and buildings. In motors, the opposite effect occurs where an electric current in a coil creates rotational motion in a magnetic field.

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