Demo of the I-V equation of an inductor

[mcastillo356]

Hello, I would like to know the demonstration of i-v formula $v=L\dfrac{di}{dt}$. Does it come from Faraday's law, $\epsilon=-N\dfrac{\Delta{\phi}}{\Delta{t}}$?; why does sometimes appears $v=-L\dfrac{di}{dt}$? . Magnetic flow in a constant magnetic field, $\phi=BA\cos{\theta}$ is also a fact that Faraday pointed out?; and also $B=\mu_0nI$?.
Self-inductance $L=\dfrac{N\phi}{I}$ for a coil is also Faraday's, or Joseph Henry's?. Is it all this empiric?; which role plays maths, calculus, and direct observation. What about $B=\mu_0nI$, is a Faradays achieve?
Thanks in advance

 

[mcastillo356]

Summary:: demo of the equation of an inductor (an electrical device, typically a conducting coil) that introduces induction into a circuit

Hello, I would like to know the demonstration of i-v formula $v=L\dfrac{di}{dt}$. Does it come from Faraday's law, $\epsilon=-N\dfrac{\Delta{\phi}}{\Delta{t}}$?

Yes, it does. From Faraday's law (described simultaneously by Joseph Henry) and selfinductance definition ($L=\dfrac{N\phi}{I}$): we know from this equation that:
1-$N\Delta{\phi}=L\Delta{I}$;
2-$N(\Delta{\phi}/\Delta{t})=L(\Delta{I}/\Delta{t})$;
3-$N(\Delta{\phi}/\Delta{t})=-\epsilon$
4-$\epsilon=-N\dfrac{\Delta{\phi}}{\Delta{t}}=-L\dfrac{\Delta{I}}{\Delta{t}}$

; why does sometimes appears $v=L\dfrac{di}{dt}$?

Sometimes we want to know this way: $|\epsilon|=|-N\Delta{\phi}/\Delta{t}|$

Magnetic flow in a constant magnetic field, $\phi=BA\cos{\theta}$ is also a fact that Faraday pointed out?;

No, is described by Ampere's circuital law

and also $B=\mu_0nI$?.

This is magnetic field inside a solenoid (coil)

Self-inductance $L=\dfrac{N\phi}{I}$ for a coil is also Faraday's, or Joseph Henry's?

It's useless information

. Is it all this empiric?; which role plays maths, calculus, and direct observation?

It's all of them

Salutes, Marcos

 

[Vanadium 50]

Why are you talking to yourself?

 

[Vanadium 50]

OK, you're sad. Again, why are you talking to yourself? What are you trying to accomplish? If we don't know what it is you are trying to do, how can we provide help?

 

[mcastillo356]

Sorry, lately I am talking to myself; I will try to be communicative with the forum. First of all, thank you for the advise, and my apology to all the people that have read this thread. It's time for me to listen to everyone that comes along.

I fear to talk again; lately I fail to put things in common with people. I really appreciate your time. Now, I will try to answer your question. Let's see: as I am studying at the spanish UNED (distance studies) to pass the exam for those aged more than 45 years, to access university. And my questions probably exceed my skills to understand the answers; I left studying maths and physics at the age of 18. I passed the exams, and started to study non scientific topics at the UPV (Public University of Basque Country).

But now I've realized that I like what I left when I was young: mathematics and physics. And I pretend to do a degree in maths. At the tenth of july are my first examinations: physics, english, spanish, and literature; I've left maths exam for september (I've only read carefully the maths textbooks, and think I've understood, with the help of everybody: teachers, forums, bibliography, google, YouTube, Wikipedia...)... The problem: I get along with the skills I must prove in july; but I want to go further; I find topics like resistance, conductivity, Ohm's law, inductance and Faraday's law, magnetic flow, Lenz's law, emf,...

The thing I pretend: to relate them, to understand the underlying physics: in this thread, I pretended to relate mathematically some of them (inductance, current flow, magnetic flow, voltage, Faraday's law...), and know everything about them. That is the real question behind my first post; the second post arrived when I saw no quick answer to my first post (now I realize why not a reply from you).

Conclusion: I go very fast; people helped a lot, showing clearly all the matter; but still insecure (the origin of some equations concern me know; specifically the relationship between Faradays law and emf equation in a coil $\epsilon=-N\dfrac{\Delta{\phi}}{\Delta{t}}=-L\dfrac{\Delta{I}}{\Delta{t}}$)

Ways you can help me: I think it was you who asked me my background: basic calculus, basic algebra...18 years old's student's knowledge, with a lack of knowledge about electromagnetism. It's my first contact.

Sorry and greetings
Marcos Castillo