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

Dens

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



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

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 travelling 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

Studiot

This subject has already been done to death here at this forum

eg

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

do a forum search for other threads

and also here

http://forum.allaboutcircuits.com/sh...t=lewin&page=3

Dens

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.