Two voltmeters in parallel measure these different voltages

[Granger]

Homework Statement

I'm currently studying induction law and circuits with inductors. I came however with the following circuit:

[1]: https://i.stack.imgur.com/ghaiE.png

Homework Equations

3. The Attempt at a Solution [/B]

Now my text says the following:

"Unlike what your intuition might tell you, oscilloscopes 1 and 2 will measure different voltages. For a N-turn coil you will get

$$u' = N\frac{d\phi}{dt}$$
$$u'' = (N-1)\frac{d\phi}{dt}$$
"

How is that possible? I'm having trouble on understanding why this results are obtained. I understand (I think) that the oscilloscopes will measure different values because the induction E field is non conservative. But I don't understand their computation. How does the left side sees one coil less than the right side?

 

[RPinPA]

I might be wrong, but if the wires are physically laid out as the circuit diagram shows, then the wires connecting up to $u''$ form a loop in the opposite direction around the coil, thus inducing an EMF in those wires which is in the opposite direction to one turn of the coil.

 

[Charles Link]

See the video in post 52 of this "link": https://www.physicsforums.com/threa...asure-a-voltage-across-inductor.880100/page-3 $\\$ What you are measuring is Professor Walter Lewin's well-known paradox.

 

[berkeman]

Unlike what your intuition might tell you, oscilloscopes 1 and 2 will measure different voltages. For a N-turn coil

I have two words for you... "Z-Lead Probes"

(Oh, and that should be "For an N-turn coil"...

http://i.stack.imgur.com/cbLXI.png

 

[Charles Link]

I have two words for you... "Z-Lead Probes"

(Oh, and that should be "For an N-turn coil"...

http://i.stack.imgur.com/cbLXI.png

View attachment 233070

@berkeman With the OP's sketch, the problem is not the leads.(It is because EMF's are being generated depending on how the wires are routed). This is a very good example of Professor Walter Lewin's paradox. Please see the video in post 52 of the "link" that I posted. Professor Walter Lewin explains it completely in his video.