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

[emroz92]

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

 

[G01]

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:

$$\vec{\nabla}\times\vec{E}=0$$

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!

 

[mikelepore]

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?

 

[Prologue]

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.

 

[emroz92]

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.