Inductor-Capacitor Circuit: E Field & Differential Equation

[atavistic]

In an inductor capacitor circuit , what is the kind of E field driving the current? Conservative or non-conservative? And I really don't understand what is the correct way to setup the differential equation for it. This is why:

In high school level textbooks(Resnick Walker), they have applied loop rule.

In Griffith, he says $$\epsilon$$ = -L di/dt = Q/C

In MIT OCW , walter lewin says $$\int$$ E.dl = -Ldi/dt = Q/C

I think last two are the same but still can someone clear this.I mean going by what griffith says(hes the best) can someone tell me why is $$\epsilon$$ = -L di/dt . I know $$\epsilon$$ = $$\int$$f.dl . How can I arrive using $$\int$$f.dl that the $$\epsilon$$ in the circuit is -Ldi/dt. This thing has been bugging me a lot, please reply.

$$\epsilon$$ = EMF and $$\int$$ = closed loop integral.

 

[nasu]

I know $$\epsilon$$ = $$\int$$f.dl . How can I arrive using $$\int$$f.dl that the $$\epsilon$$ in the circuit is -Ldi/dt. This thing has been bugging me a lot, please reply.

$$\epsilon$$ = EMF and $$\int$$ = closed loop integral.

The e.m.f is not the line integral of force but of the electric field. e.m.f is potential (work/charge) and not energy.

Another thing, it should be EMF=-L di/dt+Q/C (I mean, + rather than = between the last two terms).
It's just Kirchoff second rule: sum of the potential drops equals the EMF.

 

[sanjoser]

yep, this is getting into my question. there's a pretty good elementary discussion in this
textbook "Electromagnetic Fields and Energy" by Haus and Melcher that gets into the
difference between electrostatics and magnetostartics into the area called {electro-or magneto}
quasistatics, and how to discriminate the difference between the two. I think the differences are
pretty important in the theory of electric machines: rotating magnetic fields and all that. My primary
interest is in modeling physical circuits by extracting lumped models from gemoetric descriptions.
I'll dig out that old textbook and do some reading, maybe we can compare notes?