Faraday's Law vs Kirchoff's Rule in circuit - nonconservative fields

In summary, Kirchoff's Loop Rule has four boxes that correspond to the integral sign (\int_{a}^{b}), while Faraday's Loop Rule has two boxes that correspond to the minus sign (-\int_{a}^{b}). Kirchoff's Rule uses the integral sign, while Faraday's Rule uses the minus sign. Kirchoff's Rule applies for closed paths, while Faraday's Rule does not apply for closed paths. Faraday's Rule applies for non-closed paths.
  • #1
Dens
74
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I am trying to compare the "relation" conventions used in Kirchoff's Loop Rule with Faraday's Loop Rule.

Kirchoff

Please go to this MIT OCW link on Kirchoff's Rule and go to page 8/29. Of the four boxes, I would like to point this one

K_E.jpg


Note that the yellow electric field was added by me. This picture also follows the integral

[tex]-\int_{a}^{b} \mathbf{E}\cdot d\mathbf{s} = \int_{a}^{b} -Eds = \Delta V = \varepsilon = -IR [/tex]

Since ds and E are parallel.

Nonconservative Fields with Faraday

Now if I go to this video (I take you to EXACTLY where I want you to watch, so don't worry about searching which part of the video does this happen)

http://www.youtube.com/watch?v=UpO6t00bPb8#t=10m22s

Now quoting him

Now I go through the resistor, so I get +IR, since E and dl are in the same direction, Ohm's Law tells me I get +IR

Note that his circuit arrangement is exactly like mine, he went from a high potential to a low potential. The current, electric field in the wire, and the traveling direction are all the same, yet he gets +IR instead of -IR

is he still using this "E dot dl" [tex]-\int_{a}^{b} \mathbf{E}\cdot d\mathbf{s}= \Delta V[/tex]? How does Faraday's Law apply for non-closed paths? Because it seems like Lewin is using [tex]\int_{a}^{b} \mathbf{E}\cdot d\mathbf{s}= \Delta V[/tex] (no minus sign)

The same confusion goes when he talks about the electric field in the battery.

Could someone please clarify for me? Thank you
 
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  • #2
  • #3
Studiot said:
This subject has already been done to death here at this forum

eg

https://www.physicsforums.com/showthread.php?t=453575

do a forum search for other threads

and also here

http://forum.allaboutcircuits.com/showthread.php?t=16150&highlight=lewin&page=3

Second link wasn't very helpful and I can't pinpoint my answer in the first link because it seems like it derailed into some argument on Lewin's teaching ability.
 

FAQ: Faraday's Law vs Kirchoff's Rule in circuit - nonconservative fields

What is Faraday's Law?

Faraday's Law states that the induced electromotive force (EMF) in a closed loop is equal to the negative rate of change of magnetic flux through the loop.

What is Kirchhoff's Rule?

Kirchhoff's Rule, also known as Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL), are two fundamental principles used to analyze electrical circuits. KVL states that the sum of all voltage drops in a closed loop is equal to the sum of all voltage sources in that loop. KCL states that the sum of all currents entering a node is equal to the sum of all currents leaving that node.

How are Faraday's Law and Kirchhoff's Rule related?

Faraday's Law and Kirchhoff's Rule are both used to analyze electrical circuits. Faraday's Law is used to calculate the induced EMF in a circuit due to a changing magnetic field, while Kirchhoff's Rule is used to calculate the voltage and current in a circuit.

What is the difference between conservative and nonconservative fields in circuits?

A conservative field is one in which the work done in moving a charge from one point to another is independent of the path taken. In other words, the work done is only dependent on the initial and final positions of the charge. In contrast, a nonconservative field is one in which the work done is dependent on the path taken. In circuits, nonconservative fields can arise due to factors such as resistance, inductance, and capacitance.

How do Faraday's Law and Kirchhoff's Rule apply to nonconservative fields in circuits?

In nonconservative fields, the calculations for voltage and current using Kirchhoff's Rule may differ from the calculations using Faraday's Law. This is because Kirchhoff's Rule assumes a conservative field, while Faraday's Law takes into account the effects of nonconservative fields. Therefore, both principles are necessary for accurately analyzing circuits in the presence of nonconservative fields.

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