# Comparing self inductance of three solenoids

## Homework Statement ## The Attempt at a Solution

Self inductance depends on the geometry of the solenoid . It doesn't depend on the sense of windings . So , L1 = L2 .

But I don't understand how to deal with superconducting wires .

Does a superconducting wire affect the self inductance of a solenoid ?

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Merlin3189
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"Self inductance ... doesn't depend on the sense of windings"
What they say is, " the direction (presumably sense) of winding was reversed in each layer."

I agree with you that 100 turns CW will give the same inductance as 100 turns ACW.
But what about 50 t CW and 50 t ACW instead of 100 t in the same sense?

But what about 50 t CW and 50 t ACW instead of 100 t in the same sense?
Sorry , I don't understand your question .

Merlin3189
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Say S1 is 100 turns in a right handed sense and S3 is also 100 turns in a right handed sense.
But S2 is not 100 turns in a left handed sense. It is, maybe, 50 turns in a left handed sense, then 50 turns in a right handed sense - reversing in each layer. Or it could reverse after each 25, or after each 10. (It might complicate things if it reversed after each 30, or 20, or some number where the number of turns in each sense were different.)

So the question was, what inductance would you get if you wound 5o turns in a right handed sense and the next layer as 50 turns in a left handed sense?

To forestall another possible question: "In a right handed sense" could mean, looking at one end of the solenoid and choosing one end of the wire as the start, then the wire proceeds clockwise around the solenoid. LHS would then mean, looking at the same end and using the same starting point of the wire, you see it going anticlockwise around the solenoid.

As far as resistance goes, how do we model a real inductor?
Which parts of the model would change or stay the same in the three cases?

As far as resistance goes, how do we model a real inductor?
By considering its resistance in series with its inductance .

Which parts of the model would change or stay the same in the three cases?
L3 is an ideal inductor with no resistance .

This is what I would like to understand . How does absence of resistance affect the inductance of the coil .

Answer given is option b) . How is L3 = 0 ?

Merlin3189
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By considering its resistance in series with its inductance .
This is, sort of, what I expected. But I would say, I model a real inductor as an ideal inductance in series with an ideal resistance. (Thankfully leaving aside the capacitance for now. Real inductors are nasty little things!)
L3 is an ideal inductor with no resistance .
So L3 is an ideal inductance in series with a zero resistance.

So what are L1 and L2?

Then, what changes between the three? Obviously the resistance changes - we are told that! Why do you think the ideal inductance changes?

• Jahnavi
Merlin3189
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Just noticed your other comment, that option b) is correct. I don't understand how L3 can be 0, so you need some better help than mine.

• Jahnavi
I don't understand how L3 can be 0
Exactly @Merlin3189 and I agree that option a) is correct .But answer given is option b) .

Merlin3189
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Well, I don't agree with a) either !

The point I was trying to make, is that the resistance does not affect the inductance. That you are right in attributing it to geometry here.

My take was that,
L1 = Lx H in series with R Ω
L2 = Ly H in series with R Ω
L3 = Lz H in series with 0 Ω
And that, agreeing with your original thought, Lx = Lz, because the geometry is the same, but L2 is different because the geometry is different.

• Jahnavi
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I would go with (c), but they weren't very clear on how the direction is "reversed in each layer". Do they have an even number of layers, etc? with the magnetic fields from each layer canceling each other? $\\$ Meanwhile, inductance is defined as $L=\frac{\phi}{I}$. Clearly, it doesn't matter if the wire is resistive or is superconducting.

• Jahnavi
Merlin3189
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I agree with c) . Even if the opposing layers did not exactly cancel, that is the only answer with L1=L3≠L2

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It makes you wonder if the person who made up the problem has a misconception about the magnetic field from superconducting wire. Inside a superconductor, the magnetic field vanishes, (I believe that is called the Meissner effect), but it doesn't mean that you can't create a magnetic field by using superconducting wire in a solenoid. $\\$ Edit: See https://en.wikipedia.org/wiki/Meissner_effect

• Jahnavi
but L2 is different because the geometry is different.
L = μ0n2lA . How does sense of winding change the geometry of the coil ?

I agree with c) . Even if the opposing layers did not exactly cancel, that is the only answer with L1=L3≠L2
But how can L2 be 0 as given in the option ? It is definitely non zero .

$\\$ Meanwhile, inductance is defined as $L=\frac{\phi}{I}$
Does flux have direction ? If not then how is L1 ≠ L2 ?

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Does flux have direction ? If not then how is L1 ≠ L2 ?
The question isn't clear on what they mean by "reversed". (a) is certainly a possibility. In this case, the question is too imprecise to be worth spending a lot of effort to try to determine what is the correct answer to the question. I think we are all in agreement on our magnetism concepts in regard to the inductance from a solenoid. The question needs to be worded much better so that it doesn't lead to extra confusion for those who try to determine the answer.

Merlin3189
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Flux certainly does have direction and sense.

You can imagine L2 as two solenoids with half the turns. One is energised to be NS and the other to be SN. the two fluxes cancel out.
When wound normally, the two fluxes are in phase, both NS or both SN.

• Jahnavi
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Flux certainly does have direction and sense.

You can imagine L2 as two solenoids with half the turns. One is energised to be NS and the other to be SN. the two fluxes cancel out.
When wound normally, the two fluxes are in phase, both NS or both SN.
To reverse the direction, you would need to have a small section at the end that basically does a "U" before making the next layer. (You would need to fold the wire back on itself).

• Jahnavi
I agree with you that 100 turns CW will give the same inductance as 100 turns ACW.
Can't we just simply assume that L1 has clockwise windings and L2 has anticlockwise windings ?

Even though direction of magnetic field is opposite , magnitude of the ratio Φ/I will be same for L1 and L2 making them equal .

Merlin3189
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Can't we just simply assume that L1 has clockwise windings and L2 has anticlockwise windings ?

Even though direction of magnetic field is opposite , magnitude of the ratio Φ/I will be same for L1 and L2 .
That's correct. The question isn't clear on what they mean by reversal. (Are all of the layers reversed from the first solenoid, or do the layers alternate in the second solenoid?) And clearly, the correct answer is not (b). I think they basically goofed in a couple of places.

• Jahnavi
Merlin3189
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Can't we just simply assume that L1 has clockwise windings and L2 has anticlockwise windings ?

Even though direction of magnetic field is opposite , magnitude of the ratio Φ/I will be same for L1 and L2 .
If what you say were the right assumption, yes.
But it says the winding reverses on each layer, so they can't all be in the same direction.

The diagram I found isn't quite right. I'll look for another.

• Jahnavi
The question isn't clear on what they mean by reversal.
But it says the winding reverses on each layer
Do you agree that if the words "in each layer " are removed from the statement it would imply that the sense of windings is opposite in L1 and L2 ( if one is CW other is ACW ) ?

Would you then agree that option a) would be correct ?

• Merlin3189
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Yes.

I can't find a solenoid wound that way - I expect there is no use for one like that. The bifilar winding (intended for non-inductive wire-wound resistors) is more likely to give exactly equal and opposite inductances. If you wind one layer on top of the other, the top one has a slightly bigger area.

• Jahnavi
Glad that we all agree Last edited:
• Glad that we all agree No ! Glad that both of you agree with me Since you brought me into this discussion in post #8, can you clarify what y'all are agreeing with? I would say that $L_2=0$. There is only one choice where that is the case.