Derivation of Faraday's Law of Induction?

In summary, the conversation is about the derivation of Faraday's Law of induction from the more fundamental Lorentz Force. The person asking the question is looking for a derivation starting from the ground up, while the available proofs on Wikipedia start with Faraday's Law. They also mention a thread on the Physics Forums with a potentially helpful title.
  • #1
iScience
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I was wondering if someone could show me the derivation of Faraday's Law of induction from the more fundamental Lorentz Force.
 
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  • #3
Thanks, I saw this earlier when looking for the answer myself. I'd hate to be picky, but I'm looking for a derivation starting from the ground (Lorentz) up while the proof on wiki was more of a.. plug and chug.

the page refers to some other approaches but the two available ones both start with faraday going backwards.-----------

originally i was looking at a speaker coil and applied the RH rule just out of habit, then i noticed the direction of force predicted by the Lorentz's Law wasn't what was happening. since the Lorentz law is more fundamental i wanted to explain faraday's with it.
 
  • #5


Sure, I would be happy to provide a brief explanation of the derivation of Faraday's Law of Induction from the Lorentz Force.

First, let's start with the Lorentz Force. This is a fundamental law in electromagnetism that describes the force exerted on a charged particle moving through a magnetic field. It can be written as:

F = q(E + v x B)

where F is the force, q is the charge of the particle, E is the electric field, v is the velocity of the particle, and B is the magnetic field.

Now, let's consider a loop of wire placed in a magnetic field. As the magnetic field changes, it will induce an electric field in the wire. This is known as electromagnetic induction. The induced electric field can be calculated using Faraday's Law of Induction, which states that the induced electric field is equal to the negative rate of change of the magnetic flux through the loop:

E = -dΦ/dt

where E is the induced electric field, Φ is the magnetic flux, and t is time.

To derive this equation from the Lorentz Force, we can consider a small section of the wire with length dl and charge dq. As the wire moves through the magnetic field, it will experience a force given by the Lorentz Force equation. This force can be written as:

dF = dq(v x B)

where dq = qdl is the charge of the small section of wire.

Now, we can integrate this force over the entire loop to get the total force on the loop:

F = ∫ dq(v x B)

Next, we can use the definition of current, I = dq/dt, to rewrite this equation as:

F = I∫ dl(v x B)

This integral represents the magnetic flux through the loop, Φ = ∫ B·dl. Therefore, we can rewrite the equation as:

F = IΦ

Finally, we can substitute this into the original Lorentz Force equation and rearrange to solve for the induced electric field:

E = -dΦ/dt

And there you have it, the derivation of Faraday's Law of Induction from the Lorentz Force. I hope this explanation was helpful.
 

1. What is Faraday's Law of Induction?

Faraday's Law of Induction is a fundamental law in electromagnetism that describes the relationship between a changing magnetic field and an induced electric current. It states that the magnitude of the induced electromotive force (EMF) is directly proportional to the rate of change of the magnetic field.

2. Who discovered Faraday's Law of Induction?

Michael Faraday, a British scientist and inventor, discovered Faraday's Law of Induction in the 1830s. He conducted a series of experiments involving moving magnets and coils of wire that led him to formulate this law.

3. What is the mathematical equation for Faraday's Law of Induction?

The mathematical equation for Faraday's Law of Induction is: EMF = -N(dΦ/dt), where EMF is the induced electromotive force, N is the number of turns in the coil, and dΦ/dt is the rate of change of the magnetic flux through the coil. This equation is also known as the Faraday's Law equation.

4. What is the significance of Faraday's Law of Induction?

Faraday's Law of Induction is significant because it explains how electric generators and transformers work, which are essential components in our modern-day electricity production and distribution systems. It also helped to establish the concept of electromagnetic induction and paved the way for the development of many other important principles in electromagnetism.

5. How is Faraday's Law of Induction applied in real-life situations?

Faraday's Law of Induction is applied in various real-life situations, such as power generation, electric motors, transformers, and many types of electronic devices. It is also used in technologies like wireless charging, electromagnetic braking, and induction heating. Additionally, this law is crucial in understanding the behavior of electromagnetic waves and their interactions with matter.

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