Okay, so I got thinking after reading all your posts and I thought, let me start at the beginning. So here's the story:
We have an RLC circuit, the wires of which are along an Amperian loop. Now, the changing B-field through the coil produces a non-conservative E-field, directed tangentially to the loop at all points (basically the shape of the circuit--a closed loop E-field). Now, the charges rearrange themselves to produce instantaneous conservative E-field to cancel the induced one.
Now, I'm a positive charge--say a proton-- sitting on the battery. I start my journey through the circuit. First, the battery gives me some potential. During my journey, I encounter an induced electric field that is always in the direction I'm going. (side note: I think E
induced should be (L*dI/dt)/length of the entire loop, irrespective of its geometry). As I move along, this E-field keeps taking away more and more of my potential. There is another, conservative E-field in my way, but its effects cancel entirely by the end of my journey. I encounter a resistance, that reduces my potential a bit, and a capacitor which does the same. By the time I have reached back to where I started, my potential is L*dI/dt less than what it was when I started.
Clearly $$\oint_C E \,dl$$ =L*dI/dt
Three observations:
1. What is so special about the ends of the inductor? It seems to me that wherever you place the ends of a voltmeter (one that measure the scalar potential, as
@Charles Link and
@Delta² agree), it should measure the same p.d.--L*dI/dt, provided there isn't a battery, capacitor or resistor in between. What kind of conservative field would produce a gradient with same same p.d no matter which two points you choose to measure it between?
2. Let's say the length of the Amperian loop is
s Since the induced field, (refer to side note above) is
(L*dI/dt)/s at every point. The difference in potential at the ends of the inductor should be $$\int_{}^{} E. dl$$ which comes out to be
s'(L*dI/dt)/s, where s' is the length of the inductor's wire.
3. This elusive conservative E-field, must also be in a loop, except for a few chinks (where the capacitor, battery etc are). What the heck kind of charge distribution would produce this crazy field?
So, what say you?
Dazed and confused
OnAHyperbola