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How wrong for so long.


Blake Taylor
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The ubiquitous conventional graphic for a magnetic field through and around a cylindrical coil shows equidistant parallel lines through the central zone which it proclaims is a uniform magnetic field.

We know that field strength fades proportionally to distance from a conductor therefore the graphic field lines should show this but they don’t. The field shown is partially uniform since the lines are parallel, but the force on a charge particle diagonally transversing a gap between two aligned opposite pole coils is initially zero, then rises in the middle, then  falls back to zero as it approaches the other side. It is near hyperbolic.

Science uses the same word ‘uniform’ to describe the magnetic field across a small gap between two aligned opposite pole magnets or cored solenoids. This one is true uniform as it exerts a uniform force on a charge particle transversing the gap which a cloud or bubble chamber show as helical.

This seemingly trivial 'uniform’ error, which somehow escaped notice from academia for over a century, has been seriously detrimental to analysis of magnetism.

magFieldBoth.JPG

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28 minutes ago, Blake Taylor said:

We know that field strength fades proportionally to distance from a conductor therefore the graphic field lines should show this

It's a long time since I did any physics, but the problem I see with that is that the field in the two dimensional diagram is being created by the wiring on both sides. So as the distance from one wire increases, the distance from the other side decreases, so there's no reason why the field shouldn't be relatively uniform. The same works for 3d, I would have thought.

Probably wrong, you would have to do the maths to get it right.

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3 hours ago, Blake Taylor said:

 

The ubiquitous conventional graphic for a magnetic field through and around a cylindrical coil shows equidistant parallel lines through the central zone which it proclaims is a uniform magnetic field.

We know that field strength fades proportionally to distance from a conductor therefore the graphic field lines should show this but they don’t.

If one solves the equation for an infinite solenoid, one finds that the field inside is, indeed, uniform. The contributions from adjacent wires counteracts the drop-off from any single wire. As long as you are in a situation where the infinite appoximation holds, the field will be pretty close to uniform.

 

3 hours ago, Blake Taylor said:

The field shown is partially uniform since the lines are parallel, but the force on a charge particle diagonally transversing a gap between two aligned opposite pole coils is initially zero, then rises in the middle, then  falls back to zero as it approaches the other side. It is near hyperbolic.

Science uses the same word ‘uniform’ to describe the magnetic field across a small gap between two aligned opposite pole magnets or cored solenoids. This one is true uniform as it exerts a uniform force on a charge particle transversing the gap which a cloud or bubble chamber show as helical.

This seemingly trivial 'uniform’ error, which somehow escaped notice from academia for over a century, has been seriously detrimental to analysis of magnetism.

magFieldBoth.JPG

"Analysis of magnetism" involves the application of equations, and I don't see any here.

 

 

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There are two conditions for uniformity.

1) The solenoid has to be be of infinite length.

2) The coils or turns have to be close wound.

The first is usually approximated by saying a long solenoid.
If the solenoid is not long then it is called a short solenoid and should be so specified.

The second is specified by saying a closely wound or tightly wound solenoid, and a loosly wound one is often called an open solenoid.
The second condition can be relaxed more than the first.

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5 hours ago, Blake Taylor said:

This seemingly trivial 'uniform’ error, which somehow escaped notice from academia for over a century, has been seriously detrimental to analysis of magnetism.

How does a simplified diagram become detrimental to the analysis of magnetism?

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Diagram shows the force from parallel vectors of current in the loop acting on the straight conductor which would if it were flexible bend it into a parabola in the plane of the loop. If the conductor had ten or an infinite number of loops either side the result would much the same. This is high school stuff.

Clearly this trans axial force is not uniform, however because of the parallel non divergent lines the force, the axial aligned force on a test iron dot at any point in the coil is uniformly zero. This single aspect does not justify calling it the field uniform.

loop on conductor.JPG

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13 hours ago, Blake Taylor said:

Diagram shows the force from parallel vectors of current in the loop acting on the straight conductor which would if it were flexible bend it into a parabola in the plane of the loop. If the conductor had ten or an infinite number of loops either side the result would much the same. This is high school stuff.

If by "high school stuff" you mean that it does not include calculus, then you might have an element of truth in your statement. If you integrate the effects of a single loop over an infinite length, you get a uniform field. But you might not realize that if you can only apply high school thinking to the problem.

The practical reason I don't believe you is that I have used coil systems in atomic clocks. The C-field coil (basically a long solenoid) and the anti-helmholtz coils (coil pair with anti-aligned current) used for atom trapping behave as expected. That is, the C-field is uniform as long as you are away from the ends of the coil. If it wasn't, the clock performance would be compromised, as atoms would not experience the same field, and would thus have a different bias from the Zeeman shift that depended on their radial location. But this isn't a problem.

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On 10/28/2019 at 11:18 PM, Blake Taylor said:

 

 

This seemingly trivial 'uniform’ error, which somehow escaped notice from academia for over a century, has been seriously detrimental to analysis of magnetism.

 

I can't figure out how you conclude this.  My old physics textbook clearly states that the magnetic field within a wire coil is "NOT uniform."

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Swansont's  actual day to day experience says it is.

Which are you going to believe?

Incidentally, if you want the "high school science" explanation, remember that lines of force repel one another.

So they spread uniformly through the bore of the solenoid in order to keep as far from eachother as possible.

Why would they not?

 

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2 hours ago, John Cuthber said:

Swansont's  actual day to day experience says it is.

Which are you going to believe?

Incidentally, if you want the "high school science" explanation, remember that lines of force repel one another.

So they spread uniformly through the bore of the solenoid in order to keep as far from eachother as possible.

Why would they not?

 

John; Therefore the lines of force between two parallel conductors with opposite currents also spread out also uniformly???which a Hall effect probe would indubitably show???

OldChemE; did your book also show equidistant spaced parallel theoretic lines of force thru the mid-coil zone?

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You were asked for some mathematics, but I only see a flippant comment about high school and a diagram that is too small to read.

I do wonder if this use of the term uniform is one of degree, similar to that of 'unform velocity profile' in fluid mechanics or 'uniform stress distribution' in elasticity.

In both cases the profile is flat (uniform) over most of the cross section, with large deviations over a very small part of the outer edges.

As regards the mathematics, the conventional derivation, via the Biot Savart Law,  by extending from a single coil, only has an analytical solution on axis.

This is a fairly simple integration and leads to the conventional conclusion when appropriate limits are applied.

One difficulty comes when the gaps between the windings is significant compared to the winding diameter since you no longer have a contiguous/continuous structure so you cannot integrate but must sum a series, perhaps to infinity.

Even harder maths arises when you try to work along lines parallel to the axis, (ie off axis)
This leads to an elliptic integral which has no analytical solution, but must be solved numericall or experimentally.

Standard enginering texts just accept the experimental measurements that the deviation from uniform is insignificant as in the attachment below.
Note the main discussion in the attachment concentrates on the more significant longitudinal variation with less than infinite solenoids.

 

What distance, as a % of the solenoid diameter, would you class as significant ?
Your 'corrected diagram' in your first post suggests something different from observation.
So please put some figures to it, as I have done.

Slide1.JPG.7ed87d86d6445d1c1915269133419023.JPG

Edited by studiot
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11 hours ago, Blake Taylor said:

Therefore the lines of force between two parallel conductors with opposite currents also spread out also uniformly???

Did anyone say that?

As you are not providing any sort of rational or scientific argument, I will request that this thread is closed. 

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Why not just read Wikipedia?

Quote

Since we can arbitrarily change the dimensions of the loop and get the same result, the only physical explanation is that the integrands are actually equal, that is, the magnetic field inside the solenoid is radially uniform.

 

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On 10/29/2019 at 12:18 AM, Blake Taylor said:

This seemingly trivial 'uniform’ error, which somehow escaped notice from academia for over a century, has been seriously detrimental to analysis of magnetism.

!

Moderator Note

Please provide some citations regarding this "seriously detrimental" problem. It's your job to persuade the members to accept your reasoning, and that's only going to happen if you support your arguments. Waving your hands wildly is no substitute for evidence in science. 

 
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23 hours ago, swansont said:

Single loop, or a solenoid?

Mine book says non uniform in single loop, of course, but also toward the ends of a solenoid of finite length.  I think the OP has been well answered by others in any case, so this probably isn't of any importance.

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27 minutes ago, OldChemE said:

Mine book says non uniform in single loop, of course, but also toward the ends of a solenoid of finite length.  I think the OP has been well answered by others in any case, so this probably isn't of any importance.

And that’s correct. It’s not uniform if it doesn’t look much longer that it is wide (i.e infinite becomes a bad assumption), which happens near the ends.

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