About fem produced by coil

[Poldo]

Morning.
I would like to speak about the EMF induced by a magnetic field in a coil.
I refer to the formula fem = d(NAB)/dt
In all texts is always something about an A or a B variable with the time, but nothing about N.
I would like to know if above mentioned formula is still valid in this evenience: fem= AB dN/dt.
I mean: If the area of coils and magnetic field are constant and only the number of coils is time variant, the formula is still valid?
Thanks for the replay

 

[btrueblood]

Typically N and A are the fixed variables, and the B field changes with time. There is a type of rail gun that has coils that are destroyed by the EMF pulse, and there the A and N terms do change with time. For multiple things varying with time, you need to review your calculus III theory to take the total derivative, from memory, something like d(NAB)/dt = NA d(B)/dt + NB dA/dt + AB dN/dt, but don't trust my memory (I don't).

 

[electricpete]

something like d(NAB)/dt = NA d(B)/dt + NB dA/dt + AB dN/dt

I agree with that in terms of calculus.

Out of curiosity, what is the physical situation that is being studied ?

=====================================
(2B)+(2B)' ?

 

[Poldo]

Thanks...

I know that typically N and, sometime, A are fixed... this is why i'm asking to the forum

I'd like to vary only N, not A.
Then the formula should be emf = AB d(N)/dt
And, because the change is as step function, I should have an impulse as emf.
I tried with due coils (of 500 turn each) connected in serie and with B, generated by fixed magnet.
I saw it on a low-cost oscilloscope, but unfortunally there was so much ground noise that I can't appreciate the result.
The spikes seem to be there..but... I'm not sure.


The idea is only about experience that I would use to teach something to my granddaughter.

 

[IRstuff]

I don't get how you think you are changing the number of turns as a derivative of time.

TTFN
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[Poldo]

Hei... one step at the time!!!!
This is the second step!!!

The first step is: "Is the formula valide?".... if yes, we can go haed on the second step: "How?"...
At the moment we can suppose (this is real situation till now!) use a tumbler electrical switch ("current reverser", I think is the right translation)... Switching the "reverser", go and back, we can obtain a "like" function on N depending by t.

 

[electricpete]

Make a C core with a cap that includes a permanent magnet to drive flux around the core (flux in air neglibile).
Wrap turns of wire around the core.
Connect voltmeter to measure voltage in the coil
Use a switch to swap polarity of the voltmeter connections.
If break before make switch, voltage is zero before and after the swap.
If make before break switch (doesn't mattter,not currrent is flowing), would be zero before during and after the switch.

That's my thinking. Why should it be any different?


=====================================
(2B)+(2B)' ?

 

[electricpete]

correction in bold

Make a C core with a capgap that includes a permanent magnet

=====================================
(2B)+(2B)' ?

 

[electricpete]

The logical flaw of assuming a voltage from d/dt(N) or from switching are discussed in 6.3.6(b) and (c) here:

http://ocw.mit.edu/resources/res-6-...book-contents/chapter6.pdf?wwparam=1370379450

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(2B)+(2B)' ?

 

[Poldo]

Sorry, I didn't understand these sentences:
"If break before make switch, voltage is zero before and after the swap.
If make before break switch (doesn't mattter,not currrent is flowing), would be zero before during and after the switch."

Anyway, a Voltmeter doesn't show nothing. The emf is very low and the change very fast!!!! (If it is!)

My idea is:
The actual formula is d(B*A)/dt... then we use A= N*A1 (more turn of a small area A1)... then if I can add or remove some turn, I vary the total area (then A is variant) concatenated with the B flux... then I have to obtain emf (even if the B is constant)!!!!
More or less like the example of the C wire with a side moving in a constant B field (that varies the A).

In the oscilloscope I saw little spikes (impulses) any time that I vary the N. But I am not able to verify if these are noise (during the change the circuit is an open circuit!!!) or they are actual impulse (derivative of the step variation on N). In effect I saw the pulse is positif or negative depending by the action on N (add o subtract).

Anyway...I will read the Chapter6... Thanks...

 

[IRstuff]

Is this for school? The EMF equation has already been proven.

TTFN
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[btrueblood]

Yes, the change will be very fast. Somewhere (probably at the switch contacts) an arc is formed when you try to change N (at least, by removing coils). The step change that results from switching out a loop of the coil means that some energy must be added or removed from the magnetic field. You might see the pulses better, and extend the life of the switch contacts, by spreading them out in time: use a backwards diode or diode+zener combination to snub the back-emf.

 

[electricpete]

I’m with IRstuff, there is nothing to discover here. Consult the textbooks and you should be able to explain what you see.

Sorry, I didn't understand these sentences:
"If break before make switch, voltage is zero before and after the swap.
If make before break switch (doesn't mattter,not currrent is flowing), would be zero before during and after the switch."

Because the scenario I outlined in 4 Jun 13 15:4 involves constant magnetic field and no moving conductors.
Hookup your voltmeter whereever you like, you should measure zero volts. If you happen to short together two points of the circuit during the course of the measurement (make before break) it has no consequence, there will be no current flowing in the shorting lead, all voltages still measure zero.

I would like to know if above mentioned formula is still valid in this evenience: fem= AB dN/dt.

Based on reviewing Zahn.... No, not valid.

I refer to the formula fem = d(NAB)/dt

I don’t think this is a formula to consider valid in general cases such as N is function of t.

Faraday’s law is Equation 1 of the link (from Zahn):
Integral V = {E dot dL} = -d/dt {Integral B dot dA}
where left integral is taken around a contour C and right integral is taken on a surface S bounded by C (with relationship between polarity of S and C described in figure 6-2).

What is result when applied to time-varying contour C(t) and surface S(t) by calculus evaluation is not straightforward imo. There may be simpler versions that can be derived under specific assumption such as V = N*A*d/dt(B) for fixed non-moving conductors but nowhere does V(t) = d/dt{N(t)A(t)B(t)} appear.

It is interesting that in section 6-3-1 Zahn chooses to derive the speed voltage term not directly from Faraday’s law but from requirement that behavior in different inertial reference frames obey the same laws. Most people would probably say this is a natural and straightforward result that can be derived directly from Faraday’s law without resorting to reference frame theory, but Zahn is more cautious and chooses his reference frame approach instead. And Zahn does not jump to a sweeping generalizations about speed voltage but instead describes expected results for individual physical configurations (so as to avoid misinterpretation from looking at math equation without corresponding physical picture).

As Zahn cautions in section 6-3-6 “Faraday's law is prone to misuse, which has led to numerous paradoxes [incorrect conclusions]. 6-3-6 describes three paradoxes which are apparently highlighted because they represent ways that people are commonly prone to misinterpretting Faraday’s laws. 6-3-6(2) and (3) are exactly the items you brought up. If you look at the various sub-examples under (2=switching) and (3=change in turns), the only sub-examples where voltage is produced are where the “switching” or “change in turns” results in change in B.

My idea is:
The actual formula is d(B*A)/dt... then we use A= N*A1 (more turn of a small area A1)... then if I can add or remove some turn, I vary the total area (then A is variant) concatenated with the B flux... then I have to obtain emf (even if the B is constant)!!!!
More or less like the example of the C wire with a side moving in a constant B field (that varies the A).

In the oscilloscope I saw little spikes (impulses) any time that I vary the N. But I am not able to verify if these are noise (during the change the circuit is an open circuit!!!) or they are actual impulse (derivative of the step variation on N). In effect I saw the pulse is positif or negative depending by the action on N (add o subtract).In the oscilloscope I saw little spikes (impulses) any time that I vary the N. But I am not able to verify if these are noise (during the change the circuit is an open circuit!!!) or they are actual impulse (derivative of the step variation on N). In effect I saw the pulse is positif or negative depending by the action on N (add o subtract).

I assume you are talking about Figure 6-24(c)? (supporting 6.3.6(c))
The remainder of my comments will assume that is what you are referring to.

That case Fig 6-24(c) has no voltage source, no current following prior to changing lead position in an area of no flux outside the core, constant B.

The equation he uses to analyse that situation is NOT v(t) = d/dt {N(t)*B(t)*A}
He uses
v(t) = N(t) * d/dt {B*A} where B and A are constant in this case
That makes perfect sense... it is simply number of turns (at any time) multiple by volt per turn.
As he shows, voltage per turn is zero, so v(t) = N(t) * 0 = 0.

If you are seeing a voltage, I can suggest some possible causes:
1 – as you alluded you have an open circuit for a period of time. Voltage would be undefined/meaningless during that time... might look like a spike.
2 – there could be tiny meter current flowing... then it’s a different problem.
I’d vote 1.
Describe more about your test setup for better responses.


=====================================
(2B)+(2B)' ?

 

[electricpete]

Also worth thinking about N(t) is not a continuous function of t.
It is not appropriate to apply derivative.

When Zahn write relationship similar to
v(t) = N(t) * d/dt {B*A}
I would interpret what he is really saying is that we break the problem into interval when N is constant. For example N may be N1 during period 1, N2 during period 2, N3 during period 3.

So during period 1 we have
v(t) = N1 * d/dt {B*A}

during period 2 we have
v(t) = N2 * d/dt {B*A}

during period 3 we have
v(t) = N3 * d/dt {B*A}

It is just shorthand notation to summarize this as:
v(t) = N(t) * d/dt {B*A}



=====================================
(2B)+(2B)' ?

 

[electricpete]

Sorry to add to the conflusion.
All my comments about 6-24c were really describing 6-24a. i.e. no currents flowing. Constant source of flux like a magnet.

6-24c looks a little more complicated but still indicated as no voltage.

I'll wait for you to describe your test.

=====================================
(2B)+(2B)' ?

 

[Poldo]

Thanks for your comment.
Sorry, I can't answer now (I'm out of home). I will ansewr and try to explain better my problem (and confusion) on saturday.

 

[Poldo]

Good w.e. to all of you!

I try to better explain my logic (?... confusion, mistake???? )

I know that moving Test Point along a spiral does not generate emf (in this case we move only measuremnt point but A and B remain constant!)

With reference to the fig.6.5 (pag.400) we can see that, in constant B, moving one side of the loop we increase the flux (B*A). Right? Then we have emf generated. The formula emf= B*dA(t)/dt is working!

My exercise is:
we have a spiral S of N loop of area A (head of wire called 1 and 2) and an other spiral S1 of N1 loop of same area (head of wire called 3 and 4).
Then in each spiral we have B*N*A and B*N1*A flux (we can call them F and F1)
We start with a voltmeter connected to the 1 and 4 points.
If we connect and disconnect, by a switch, this two spirals in serie (connecting 2 and 3 points) obviously we don't measure emf (the total flux doesn't change Ft=F+F1 at any time)

But if we interpose between the 2,3,4 terminals a device (inverter switch, call it D and its terminal D1 and D2) we can obtain:
( the "->" means short-cut)
First position of switch:
Point 1 - coil - Point 2 -> D1 -> Point 3 - coil - Point 4 -> D2

Other position of switch:
Point 1 - coil - Point 2 -> D1 -> Point 4 - coil - Point 3 -> D2

Because the flux has a sign, in the first position we have Ft'=F+F1 but in the second we have Ft"=F+(-|F1|)

Then we obtain a Delta of flux... then I aspect an emf due to the dF/dt.
And because to the step variation I aspect a pulse emf (positive or negative) that is what seems what I see on the low-cost oscilloscope.

Where is my conceptual mistake?

 

[Poldo]

Another concept:
I don't "create" nothing!!!
I spend work to move the switch, then it is possibile that I obtain emf from that work

 

[IRstuff]

Your experiment can easily be done by running a center-tapped transformer.

TTFN
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[Poldo]

Sorry, but (if I have well understood what a "center-tapped transformer" is) there is not inversion of flux on it. All the concept is based on clocck-wise and counter-clockwise turn of coils... that varies the total area of the spiral