lab electromagnet from scratch

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Rich Feldman
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Re: lab electromagnet from scratch

Post by Rich Feldman »

In case the pictures are misleading: Yoke parts in BTI have areas that are 113% and 122% of the pole area, counting both legs. So yoke metal is always farther from saturation than pole metal. I think the corresponding area ratio in the Mullins magnet (MCM?) is 95% for both part types.

The exceptionally slender aspect ratio comes from 1) need to reach around two coils with >10K ampere turns each. That's the minimum to get 1 tesla in 1 inch of air, for any pole diameter. Plus roughly 6% to magnetize about 1 lineal meter of steel to similar B value, same as in MCM. And 2) keeping the pole area down to facilitate DIY steel fabrication and handling, since no minimum diameter was required. I still believe this would be hunky dory if not for the leakage flux challenge.

Thanks for all the hints. After some reading, thinking, and just a little computing, my grasp of leakage flux is much better than it was a few days ago. The Internet teaches that all electromagnets and transformers have leakage flux percentages. It helps to keep air gaps narrow (duh!). And if wide, to place the coils as close as possible to the gap.

Some simulations, and multi-point flux measurements (with various gap lengths), are in the planning stage.

I bet they will support the view that in this application, aspect ratios are what matter most. Permeability is second, and nonlinearity (saturation) is last.

Let's assume the core's top half is a mirror image of the bottom. Take the magnet's nominal size (pole diameter) as the unit of length. I claim that the dimensions which matter most are air gap length, pole length, and radial distance between pole and "side bar". The last two are driven by coil length and diameter. The numbers for MCM appear to be in the mainstream -- about (0.24, 1, 1). For BTI they are (0.33, 2.33, 1.5).

For simplicity, keep B enough below saturation that the steel B-H curve is still sort of linear. Then we can look at the B/2 field generated by bottom coil only. Later superimpose a mirror image to get the total field.

Consider the flux impelled upward by the lower coil, when it reaches the bottom pole surface. If there's no air gap, the least reluctant return path is to carry on into the upper pole piece, and come back around the yoke. Nothing but steel! Total reluctance is low, and so is the total MMF for a design amount of flux. The "magnetic potential" is distributed around the whole circuit, so a small fraction of the flux will take a short cut through air from the pole pieces to the yoke.

It doesn't take much of an air gap to greatly raise the magnetic potential difference between the two pole surfaces, and demand lots more ampere turns. Now as the flux emerges from lower pole, the upper pole surface isn't so inviting. The yoke bars are still on the far side of some air, but their broadside view presents plenty of area.

I think simulations (and measurements) will show that when the air gap reaches 1 inch, between 3 inch diameter poles, the total reluctance of sideways leakage paths is less than that of the air gap itself. Both are much larger than the reluctance of the intended flux path through steel. Yoke bars could all be twice as thick, or twice as permeable, without greatly reducing the leak percentage. If 3D simulation were available, we might see if it helps to place my side plates with narrow edges instead of broad faces oriented toward the pole axis.

And that's one man's novice opinion.
All models are wrong; some models are useful. -- George Box
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Rich Feldman
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Re: lab electromagnet from scratch

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Been talking with Chris, but haven't yet updated the MCM coil dimensions from guesses in this picture.
Discovered a cool way to name the nodes in one-dimensional magnetic path model.
bti_mcm1.PNG
In the round parts, blue lines are drawn where they bisect the semicircle area. :-) Chris, should the NS order in MCM figure be flipped?

Sketch at the top left shows axisymmetric model of BTI for the first FEMM simulations. Left edge is the axis of rotation. Yoke horizontal and vertical bars are represented by disks and a thick tube with the same cross-sectional areas (still 113% and 122% of pole area). So the model is configured like a gapped ferrite pot core. I bet it will overestimate leakage flux.

Between the poles, FEMM model has a few very short cylinders that can be steel or air.
bti1a.PNG
Here there's a 0.1 inch air gap, which gives a nice qualitative view of leakage flux. Only the bottom coil (with practice coil dimensions and turns count) is energized. That makes it easier to understand the leakage flux behavior. If we were to add an identical top coil, it would superimpose a mirror-image field distribution, restoring top/bottom symmetry at the gap.
bti1c.PNG
Since BTI's design target doesn't specify the strong field diameter, I'm thinking about tapered pole ends. Time to stop pinching pennies so hard, and shop out some of the fabrication work. Cost to date is under $100 for all parts in the picture, including extension cord and four casters. I've probably spent more time talking about it than working on it.
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Rich Feldman
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Re: lab electromagnet from scratch

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Couldn't resist posting more axisymmetric simulation results, before trying a planar model of the same real object.
When there's no air gap, there's practically no leakage flux. 1-D model would be quite accurate. The new chart is |B| along a contour from bottom to top, at half of the pole radius. Current is 1 ampere in the extension cord coil.
bti2b.PNG
With a half-inch air gap, the peak B is vastly smaller (as predicted by 1-D model), and gap B is even smaller by another factor of three.
bti2a.PNG
Let's see what happens when we increase the vertical yoke bar area from 1.22 to 2.35 times the pole area.
bti3a.PNG
Not much, eh? Tends to confirm that this is a pole aspect ratio thing. Of course we need to repeat the experiment on a traditional, stubby geometry like MCM. Maybe Chris will beat me to it.
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Rich Feldman
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Re: lab electromagnet from scratch

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Tried insulating the sideways leakage path with a sheet of superconductor. Set u = 0.001; maybe zero would work. Pattern changes, but the flux still finds ways to leak around the desired gap.
bti3i.PNG
A simulation with tapered pole tips also revealed little improvement, a finding that initially came as a surprise. Needs more review & thought, but much easier than having to turn a few pounds of steel into swarf.

Then came a planar-geometry model of BTI. Yoke part widths are fudged differently, to keep the cross-sectional area ratios right. All flux is parallel to the plane of the paper. (As in the axisymmetric model, where the plane is any that includes the axis.) I think the planar model underestimates leakage and fringing flux; the axi. model would be good about fringing but very pessimistic about sideways leakage.
btip1.PNG
The planar problem size could be halved, with the right boundary condition applied at the line (plane) of bilateral symmetry. The round shells were set up by a FEMM wizard, as a boundary condition to emulate unbounded space.

This calls for lab measurements. I've wound a round fluxmeter sense coil to fit around pole pieces. Got the bobbin made for a rectangular one, to fit yoke side bars. Sensitivity calibration is easy & very accurate. Rectangular coil will have 10.00 +/- 0.01 turns. Round coil also has 10 turns, with a tap at 5 turns.
The tap will allow direct comparison of flux in one sidebar with half the flux in a pole piece, without changing the instrument range or doing arithmetic. Come to think of it, the sense coils could be connected in series to read the difference between pole and sidebar fluxes. Then slid vertically to find null places (height pairs where pole and side fluxes are equal). No fancy voltage integrator needed for that!
All models are wrong; some models are useful. -- George Box
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Re: lab electromagnet from scratch

Post by Mark Kimball »

If you are not already using it, I have found FEMM's scripting capability (via LUA) to be useful for playing with different magnet configurations. It can speed things up quite a bit compared to manually setting dimensions of your parts (or coil currents etc.). It can take a little time to write functions to create components with rectangular and cylindrical profiles, but after that it is much less painful to experiment.

Mark
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Re: lab electromagnet from scratch

Post by Chris Mullins »

Mark, I can second the recommendation for FEMM's Lua scripting - it was very easy to that working.

I simulated the "MCM", as Rich has named it, this weekend. Two immediate observations: 1) FEMM works pretty well, and 2) I should have simulated the MCM before actually building it.

I drew a 2D slice of the MCM, not accounting for the roundness of the pole piece. My first question was how the field in the gap varies with current, especially considering my plans to upgrade from the 3kW (55A) I have now to 5kW and even 10kW (75 or 100A of coil current). My original design calculations used the simple formula of B = 4*pi*N*I/G, where B is field strength (Teslas), N is number of coil turns, I is current, and G is gap width. Clearly that will overestimate the field when the iron starts saturating, but I didn't simulate that. At my full current of 55A, I get this from FEMM:
mcm_2coil.png
which shows about 860 mT in the gap, compared to 976 mT predicted by the simple formula.

Using Lua, I scripted the coil current ramping from 5A to 100A in 5A increments, and extracted the field at the center of the pole gap. The script is pretty simple:

Code: Select all

showconsole()
mydir="./"
open(mydir .. "mcm_2coil.fem")

mi_saveas(mydir .. "temp.fem")
clearconsole()

for n=0,100,5 do
  mi_modifycircprop("bottom coil",1,n)
  mi_modifycircprop("top coil",1,n) 

  mi_analyze()
  mi_loadsolution()
  A, B1, B2 =mo_getpointvalues(0,10.75)
  bmag=sqrt(B1*B1 + B2*B2)
  print(n,bmag)
   end

mo_close()
mi_close()
Extracting those results from the console and plotting them along with the simple formula shows that even at 55A, the efficiency is only 85%, which is close to what I actually measured, and at 100A, it drops to 66%. My son and I set up our gauss meter as close to we could in the center of the gap, and stepped the current from 5A to 55A (as high as we can go), and plotted those on the same graph. The results match FEMM very closely:
fs_vs_current.png
The red line is the simple formula value, the blue is the FEMM output, and the green diamonds are our actual measurements. At 100A (10kW) I'd only get 1.16 Tesla, which isn't worth the effort (would take a single phase to 3 phase converter, a much larger power supply, and much better cooling). Even 5kW doesn't get very far.

The FEMM vs. measured efficiencies (ratio of actual to predicted field strength) are pretty close:
eff_current.png
I would expect the physical magnet to be worse than the simulation, given non-ideal frame flatness, small gaps, etc., and generally it was a little lower (1-2%). Some of the difference is likely measurement error too. We started by removing any remanence from the frame (typically about 15 mT), then stepping from 0A up to 55A, but our current measurement resolution was only 0.1A.

Switching the frame from 1018 steel (what I actually used) to 1006 in FEMM improves things a bit - FEMM gives me 920 mT instead of 860 mT (compared to 976 in the formula). I couldn't readily find a low cost source for any lower carbon steel than 1018 though.

Although I have both coils installed now, for a while I was running with just the bottom coil, and had noticed a difference in field strength from the face of the bottom pole to the top pole. This difference varied with position (almost none at the pole center, getting worse towards the pole edge). I simulated this with FEMM, and that also agreed with what I had seen. I used a Lua script to measure the field from pole center out to the edge, in 0.1" increments, at both the top and bottom of the gap:
field_gap_1coil.png
When I had noticed this effect earlier I noted a 2-5% difference, as measured roughly an inch or so in from the pole I (that wasn't very controlled; I was pushing my field sensor as far as it could reach in the gap between my chamber and the pole). That roughly agrees with the FEMM result. As Richard pointed out, a 72 Gauss difference out of 1449 isn't much, and could be from the asymmetry of just one coil (longer flux path), or tiny imperfections in the frame, etc. I'm sure both effects are there to an extent, but the FEMM result suggests the former is dominant here, within my measurement error. I considered disconnecting the upper coil and taking more careful measurements, but didn't get that far.

Next, I looked at the field (with both coils) at the center of the gap (vertically), as it varied with distance from the pole center to the edge. This is where any pole shape optimization would be needed to improve the cyclotron. I didn't have a quick method to vary the field probe radially from the center in a controlled, measured manner, so I don't have physical measurements to compare with. Here's the FEMM output though, from another Lua script that steps through the field measurements:
field_vs_position.png
Finally, in another discussion I mentioned attempting to measure the "DC" inductance of the magnet:
Total coil inductance is difficult to measure directly. My LCR meter only goes to 100 Hz, not low enough to get the "DC" inductance. Readings at 100, 120, and 1000 Hz are 34.3, 32.9, and 14.6 mH, respectively. A (very) rough L/R time constant measurement going from zero to 12 amps gives around 80 mH
FEMM can give the total stored energy in a magnetic field, and running that for the MCM at 55A gives 81 Joules. Working from E=0.5*L*I^2, the inductance is around 54 mH, somewhere between the 100Hz meter value of 34 mH and my (very) rough 80 mH. I suspect FEMM is closer than my estimate ....

Rich, thanks for the suggestion on FEMM - it's definitely a powerful tool, and not difficult to use once you know what to do. In case it's helpful for anyone else getting started, here's a link to the MCM FEMM model: https://mullinscyclotron.weebly.com/upl ... _2coil.fem

Maybe a brief overview of FEMM (including scripting) for electromagnet modelling would be a good post for the new magnetics FAQ?
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Re: lab electromagnet from scratch

Post by Mark Kimball »

Chris,

Wow, you really got all over that one! It is good to know that FEMM does a pretty good job of simulating electromagnets. Hopefully it's as good with NdFeB magnets because that's what I'm interested in.

-Mark
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Re: lab electromagnet from scratch

Post by Chris Mullins »

Yeah, well I did have a long weekend to work on it :)

Rich pointed out offline that I may have two flaws in my FEMM model that could be roughly canceling each other out, so that the results happen to be close to correct on some of those results. I'll try the axisymmetric model this weekend, and varying my planar model to explore that more closely.

All goes to show it's important to have a good understanding of the underlying principles, how the models work, and the expected results when using simulations. Otherwise it may be "garbage in, garbage out."
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Re: lab electromagnet from scratch

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Here's a drawing to illustrate the one-dimensional "magnetic reluctance" model which Richard Hull mentioned here. Hats off to Oliver Heaviside.
I think it can explain most of the "inefficiency" when Chris's measurements & simulations fall short of the simple B = u0*N*I/G. That formula is based on reluctance of the air gap, without consideration of that in the steel path. The formula predicts 20212 ampere-turns per tesla for a 1" air gap, but we need another 2248 ampere-turns per tesla to magnetize the steel.
reluctance.PNG
The MCM and BTI electromagnet steel parts and 1" air gaps are rendered as rectangles. Height is proportional to physical length in the magnetic flux direction; width is proportional to the cross sectional area. (So the shaded area ratio matches the mass ratio, except for square corner details.)
By analogy with electrical resistance, we can figure the reluctance of each section in ampere-turns per weber (like volts per amp).
It's equal to length, divided by cross sectional area, divided by the magnetic permeability. For air that's u0 = 4 pi / 10^7. In MS Excel, 4e-7*pi(). For steel I used a value 500 times greater (more permeable). Ampere-turns per weber is dimensionally the same as inverse henries. For wound cores like we're talking about here, I think the inductance constant L/N^2 is the inverse of the total reluctance -- if all the flux linked all the turns.

The 8" magnet has reluctance values roughly 7 times smaller than the 3" magnet, because that's the pole area ratio.
But for a given B value, the 8" magnet needs 7 times more flux (in webers). So the associated MMF (magnetomotive force) values, in ampere-turns, are roughly the same. They're identical for the 1" long air gaps and 7" long round pole pieces.

This model is accurate for very small air gaps. But it doesn't account for 2D and 3D effects: fringing flux near the gap and leakage flux between pole pieces and the yoke. I've learned that those are hugely significant for the slender magnet on the right side of picture.
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Rich Feldman
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Re: lab electromagnet from scratch

Post by Rich Feldman »

Not sure whether to dust off this old thread, or start a new one for a tangential topic.

The next step for BTI magnet project is to measure the flux distribution, quantitatively.
How will the fraction which fringes out or leaks away go up, as the air gap length increases from zero to 1 inch?

It'll be much worse for the slender geometry of BTI than for the stubby pole pieces in traditional electromagnets.
The area presented by opposite pole piece, where we want the flux to go, is much smaller.
The area presented by yoke side bars, to which the flux wants to leak, is relatively larger, and the leakage distance through air is only a few times greater than the pole-to-pole distance in original design.
I bet the magnetic reluctance of the slender steel yoke and pole pieces will be unimportant when air gap is longer than 1/2 inch. Replacing all of them with super stuff, infinitely permeable and non-saturating, would not substantially increase my air gap teslas per ampere-turn. See the reluctance model picture in this post's immediate predecessor.

Anyway ... More than a year ago, I wound a couple of fluxmeter sense coils. One sized to slip over a round pole piece, and one to slip over a yoke sidebar. They are still gathering dust, on the magnet, in my garage. Associated electrical fluxmeter instrument hasn't been fired up.
Looks like the fluxmeter will soon be turned on for a different project, that goes with this brand-new sense coil:
DSCN1859.JPG
The "former" is a bit of 2-inch Sch40 plastic pipe, with a hacksaw-width groove near one end. In the groove are five turns of 34 AWG magnet wire.

It's to quantify the strength and axial distribution of flux in a loudspeaker magnet assembly. Last week a friend gave me the part, which I guess weighs 10 or 15 pounds. Must've once had a pretty thick voice coil, since the above-pictured pipe goes in with plenty of clearance, inside and out.

It was obvious what to do first, with such a nice magnet. Demonstrate eddy current braking (drag) effects on copper and aluminum. Picture below includes a 7.5-oz Coke can, I think nominally 58 mm OD, with its bottom cut off. Dropped into the magnet gap, it settles in slowly.
DSCN1857.JPG
Nominal two-inch copper and aluminum pipes fall just as slowly. You can feel the drag when pulling them back out, and lack of drag when twisting them. The demo will be more complete when I can say how many amperes are eddying.

Forum question 1:
How will the dropping copper pipe behave differently when it has a narrow slot along its whole length?
Forum question 2, before I reset more passwords that were forgotten many years ago:
Is Youtube still a good place to share videos? How about Flickr, or Imgur? Please don't say Facebook. :-)
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Rich Feldman
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Re: lab electromagnet from scratch

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First real measurement of the radial flux density, B, indicated 0.60 teslas. That's much lower than I'd guessed at the beginning. It's roughly consistent with last night's initial SWAG, based on a copper pipe's physical parameters and rate of descent, judged by eye. I still don't know the sign, which could be checked with a magnetic compass at a safe distance.

Today's measurement is based on the lifting force from current in a voice coil. Flux measurement by integration of induced voltage will be done next.
The lifting force factor, in newtons per ampere, is identical to a loudspeaker parameter called Bl, in tesla-meters. Product of flux density B and the length of wire in the magnet gap. Ain't the SI system nice here? Some presentations found on the Internet suggest that 20 T-m is an ordinary value in powerful woofer drivers. Anybody here got experience with loudspeaker design or reverse-engineering?

My hobby lab style, as some friends know, often seeks quick gratification from materials and tools on hand. Buying new stuff, or having to clean up and find lost stuff, is no fun.
Today's "voice coil" started with a tube wound from 1-inch-wide paper, and some glue, using copper pipe as a mandrel. It has 12 turns of 26 AWG magnet wire, from a 5-lb spool that I _did_ find under cobwebs and dust.
It's driven by an adjustable DC power supply, whose digital current meter has a resolution of 0.01 ampere.
The resisting force is a stack of nickels (USA $0.05 coins) which are taken to be 5 gram weights.
DSCN1861.JPG
Picture also shows that the ferrite ring magnets are far from concentric with the steel pole parts. I drew an eccentric circle on top plate directly above the inner edge of the ferrite parts. Is that just from sloppy assembly, or is it on purpose? Could be to leave more space for some other part in original Sunfire powered subwoofer box. Like the eccentric jet engine inlets on 737's, which are to increase the ground clearance.

For N_nickels = 0 to 4, I recorded the current at which voice coil began to rise from its support.
To get the most out of the few significant digits, I let Excel figure a straight-line fit:
nickels.JPG
nickels.JPG (17.21 KiB) Viewed 9415 times
The slope works out to 1.26 N/A, which we take as the Bl value.
The average coil diameter, times pi, times the number of turns, gives us wire length l = 2.107 meters. So we infer that B = about 0.60 teslas, around the middle of the gap, at the radius of this coil.

The flux density in this magnet will be about 27% greater at the inner pole face than at the outer pole face, simply because of the radial geometry. But the force factor, in N/A, doesn't depend on the radial position of any turn in a voice coil. A turn near the outside is in a weaker B field, but has a proportionately greater length of wire, so contributes the same amount toward total "thrust". It crosses the same total amount of magnetic flux (in webers or maxwells) per millimeter of axial displacement.

This same post just went up on another forum for hobbyists, but no more than that.

[edit]Got the sign without finding a compass, or applying right or left hand rule. The magnet assembly _is_ the compass.
DSCN1863r.JPG
Suspended with axis horizontal, it turns so the annular plate (outside pole) faces magnetic south.
The inner pole is connected to end plate which faces magnetic north.
Will be fun to model this in FEMM, with enough room on the outside to see and measure the far-field dipole moment.
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Re: lab electromagnet from scratch

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Permanent magnet measurement exercise is complete. Ought to be good practice for using fluxmeter to learn about flux leakage in Big Three Inch electromagnet project.

I told the details step by step on another forum, as they unfolded: https://highvoltageforum.net/index.php?topic=819.0
That's different from the old 4hv.org forum, which has been almost abandoned for about a year. :-(
After _their_ change of software or hosting service left people unable to see old pictures or post new ones.

Here let's start with a FEMM analysis of my subwoofer magnet, whose center pole is hollow. My first use of permanent magnet material in simulation: stuff called Ceramic 5 in the material library under Hard Magnetic Materials, with no adjustment to its default magnetization strength. The FEMM exercise was actually done AFTER my first flux vs Z sweep in the lab.
fluxes6.JPG
.
Now back to the lab, whose RFL model 916 fluxmeter was presented years ago in this very thread, with this picture:
flux2.PNG
Today it's connected to the sense coil pictured about a week ago, wound at the end of a black plastic pipe that fits into loudspeaker magnet gap.

Here is a representative data point collecting procedure.
1. Set range buttons to 1 x 10^3 kilomaxwell turns.
2. Put sense coil holder all the way in. Now the coil surrounds the magnet center pole near its root.
3. Push the Reset button (of voltage integrator connected to the LED panel meter).
4. Pull sense coil all the way out (far enough for flux through it to be practically zero).
5. Read instrument digital display: 1.523. That indicates 1.523 million maxwell turns. Same as 0.01523 volt-seconds.
6. Divide by the number of turns in green-wire sense coil, 5. Result is 304.6 kilomaxwells (3.046 milliwebers).
That's the total amount of flux in center pole at its root. Average density in the steel there is 20,000 gausses (2.0 teslas).
This place is a bottleneck, because of saturation, so the radial flux in main gap can't be much more than 1/2 tesla.

Next part: repeat the reset, move, read sequence for different initial z positions.
Sense coil motion is constrained by a paper sleeve, that fits over center pole and a clear plastic extension:
DSCN1880.JPG
The flux values F(z) decline from 3.046 mWb (304.6 kilomaxwells) near root of center pole, to practically zero 14 cm above that place.
Delta F between two z values represents flux that passed out of the center pole and outward through air between those z values.
So dF, divided by the cylinder section area 2 pi r dz, gives us the radial flux density B(z).
flux_c2.JPG
The quantitative match between measurement and un-adjusted simulation is amazingly close. Random good luck? Close encounter of the third kind?
All models are wrong; some models are useful. -- George Box
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