Kirchhoff's Law Derived from Faraday's Induction - EMROZ

In summary, the conversation discusses the derivation of Kirchhoff's Voltage law from Faraday's Induction law, and the validity of the law under electrostatic conditions. The reasoning is deemed correct and it is noted that the relationship has been previously established. The conversation also touches on the validity of the law in the presence of changing magnetic flux and its connection to Maxwell's equations. Some books use Kirchhoff's voltage law under changing magnetic fields, but the conversation points out that this introduces an additional emf term that is not accounted for in the original derivation.
  • #1
emroz92
12
1
Please see the attachment. There I have derived Kirchhoff's Voltage law from Faraday's Induction law. Reply me if I have done something wrong and also notify me if this proof has been made somewhere else.

Thanking you,
EMROZ
 

Attachments

  • Kirchhoff from Faraday.pdf
    92.7 KB · Views: 304
Physics news on Phys.org
  • #2
Yeah, the reasoning is fine. What you're doing is stating the electrostatic condition for the curl of the E field.

Essentially, you're taking:

[tex]\vec{\nabla}\times\vec{E}=0[/tex]

and expressing it in integral form.

This is a well known fact. So, yes it has been done before.

Also, the validity of Kirchoff's Voltage law is not something that is questioned or "unproven." It is a direct consequence Maxwell's equations under electrostatic conditions (as you showed) or, (in my opinion ) more fundamentally, of conservation of energy.

Still, its cool that you derived this result yourself, without any knowledge that the relationship was there! These are the moments that make studying physics really great!
 
  • #3
G01 said:
under electrostatic conditions

Why electrostatic? Under what conditions, if any, is Kirchhoff's voltage law no longer correct? For example, isn't it still true if a changing magnetic flux is passing through the loop?
 
  • #4
mikelepore said:
Why electrostatic? Under what conditions, if any, is Kirchhoff's voltage law no longer correct? For example, isn't it still true if a changing magnetic flux is passing through the loop?

No, the closed loop integral wouldn't be zero. The changing flux would induce an emf and that means del cross e isn't zero.
 
  • #5
Yeah right,
Many books (Halliday, for example) use Kirchhoff's loop law under changing magnetic fields and they use $\E_{L}$ in the equation. Actually, this very emf is the right hand side of the Maxwell's equation and they toggle it to the left hand side and denote it beside the solenoid in the circuit diagram.
 

1. What is Kirchhoff's Law Derived from Faraday's Induction?

Kirchhoff's Law Derived from Faraday's Induction is a fundamental principle in electromagnetism that explains the relationship between electric currents and magnetic fields. It states that the induced electromotive force (EMF) in a closed circuit is equal to the rate of change of magnetic flux through the circuit.

2. Who discovered Kirchhoff's Law Derived from Faraday's Induction?

Kirchhoff's Law Derived from Faraday's Induction was first discovered by German physicist Gustav Kirchhoff and British scientist Michael Faraday in the mid-19th century. They independently came up with the law while studying the effects of magnetic fields on electric currents.

3. How is Kirchhoff's Law Derived from Faraday's Induction used in practical applications?

Kirchhoff's Law Derived from Faraday's Induction is used in various practical applications, such as generators, transformers, and motors. It is also used in the design of electrical circuits and in the development of technologies like wireless charging and electromagnetic induction cooking.

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

Kirchhoff's Law Derived from Faraday's Induction is significant because it helps to explain the relationship between electricity and magnetism, which are two fundamental forces in nature. It also forms the basis for many important technologies that we use in our daily lives.

5. How does Kirchhoff's Law Derived from Faraday's Induction relate to other laws of electromagnetism?

Kirchhoff's Law Derived from Faraday's Induction is closely related to other laws of electromagnetism, such as Ohm's Law and Ampere's Law. Together, these laws form the foundation of classical electromagnetism, which is essential in understanding and predicting the behavior of electrical circuits and devices.

Similar threads

I Faraday's Law Equation: Derivative vs Delta
    • Electromagnetism
Replies
2
Views
946
I B-Fields: Deriving Faraday's Law & Why No Work?
    • Electromagnetism
Replies
6
Views
733
I Reason for Opposite Signs for Terms in Faraday's Law and Ampere's Law
    • Electromagnetism
Replies
15
Views
738
Faraday's Law with Zero Resistance Current Loop
    • Electromagnetism
Replies
2
Views
6K
Some confusion of Faraday's law of induction.
    • Electromagnetism
Replies
5
Views
2K
Faraday's Law & Motional EMF Confusion
    • Electromagnetism
Replies
3
Views
2K
Transformer equation: Using Faraday's law "the wrong way"?
    • Electromagnetism
Replies
10
Views
2K
How do we show that the interior of a Faraday cage is an equipotential?
    • Electromagnetism
Replies
10
Views
1K
Faraday's law or Lorenzt force?
    • Electromagnetism
Replies
9
Views
2K
I Mutual inductance in a transformer
    • Electromagnetism
Replies
16
Views
1K

Hot Threads

Recent Insights

Back
Top