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# Field strength vs. gap between poles3

## Field strength vs. gap between poles

(OP)
I have a question about how the distance between a north and south pole effects the field strength at a point equidistant from each pole face. My college physics book seems to treat it as if it will not change with distance if the faces are infinitely large planes. Visualizing this, as long as the imaginary field lines are parallel there is no change in flux, which I believe is in line with Gauss' law(?) Is this true, and if so how does it work out in the real world? is there a ratio between the distance poles are apart and a distance from the edge of a pole that we can consider the flux uniform?

### RE: Field strength vs. gap between poles

One rule of thumb approximation is that the field starts to be "uniform" one gap distance in from the edge.

### RE: Field strength vs. gap between poles

Well, no, the magnetic induction, whose flux, as you certainly know, is constant along the magnetic circuit, is by no means constant when the gap varies.
In formula B=Br/(1+g/h), g being the gap length (total in series in the circuit) and h the length (total in series) of the the active permanent magnets with residual induction Br.
Now h, at least for modern RE magnets, is of the same order of magnitude as the gap g, say between 1 and 2 times g. From the formula above, if the gap doubles, going from 0.5h to h, the induction reduces by 75%, which is not really constant.

prex

http://www.xcalcs.com
Online tools for structural design

### RE: Field strength vs. gap between poles

(OP)
Thanks sreid & prex
I'm still learning about magnetic circuits, it's totally new to me.
This question pertains to the hobby cyclotron that I posted a question on this forum a few weeks ago. So what I'm really trying to do is calculate the radius of a particle of known mass, at a known speed in a given B field. This I can do if I know the B field, but I'm trying to figure out what the field will be at a given distance. I'm sure the formula given by prex is applicable, but I don't really understand where the h comes from or if it's applicable to my  situation. I also don't understand the concept of the B sub r, although I'll try to research it on my own, maybe it's in the freq. asked question area.
Most magnet manufacturers rate their magnet strength and are around 1 Tesla for the ones I'm looking at, but I assume that's at zero distance, which is making it difficult because I can't, for example, "double" the distance in my calcs.
If anyone can clarify it would be much appreciated.
thanks again
-Todd

### RE: Field strength vs. gap between poles

Your field strength around 1 Tesla is exactly what is called the residual induction Br.
And you are correct (good starting point for deepening your knowledge): this will be the induction in a circuit with zero gap (a totally useless circuit by the way).

prex

http://www.xcalcs.com
Online tools for structural design

### RE: Field strength vs. gap between poles

You need to look at the entire demagnetization curve.  The B vs H for your specific material will give you an idea of where you will be operating, and what B value to use for calculating field strength.

= = = = = = = = = = = = = = = = = = = =
Corrosion never sleeps, but it can be managed.
http://www.trenttube.com/Trent/tech_form.htm

### RE: Field strength vs. gap between poles

Below are equations that will make it easy (these are really the same as Prex's).  If no flux focusing is used the areas are equal.  Make PC equal to one to operate at the maximum energy product (least volume of magnet).

PC=(Lm/Lg)(Ag/Am)

Bm=(Br)(PC/[PC+1])

Bg=Bm(Am/Ag)

PC = Permeance Coefficient

Lm = Length of the Magnet

Am = Area of the Magnet

Lg = Length of the Gap

Ag = Area of the Gap

Br = Magnet flux density remenance

Bm = Flux density in the magnet

Bg = Flux density in the gap

Assumes recoil permeance is one.

### RE: Field strength vs. gap between poles

(OP)
So after sitting down with this information and working out a few samlples it seems that the loss in Br due to the gap (Lg) can be compensated for by increasing the thickness of the magnet in the direction of the poles (Lm) but one can't get back to 100% of the surface Br in the gap (at least with a simple 2 magnet circuit).
I had no idea that the magnet length had such an effect.
Am I interpreting this correctly?

### RE: Field strength vs. gap between poles

Yes, your interpretation is correct.  That's why the area of the pole pieces is often reduced to increase the flux up to, say, 1.5 Tesla maximum (limited by the magnetic saturation of the iron).

### RE: Field strength vs. gap between poles

In high field devices you end up with long back iron that has a large corss section.  The first set of pole pieces will be iron and slightly tappered.  Before you get to the saturation you will switch to an FeCoV alloy and tapper further.
At least with steady field you don't have to add the compication of laminating everything.

= = = = = = = = = = = = = = = = = = = =
Corrosion never sleeps, but it can be managed.
http://www.trenttube.com/Trent/tech_form.htm

### RE: Field strength vs. gap between poles

(OP)
So does a magnetic circuit have to be "closed" in order to as Prex said count the magnet length for the entire ciruit?
for example:
If I have just (2) 1.2 Tesla Br RE magnet disk assemblies (probably 15cm Dia) which are each 2cm thick, and are held apart 1cm
using B=Br/(1+g/h)  and SI units

B=1.2/(1+.01/.04)= .96T

or is it

B=1.2/(1+.01/.02)= .08T  ?

Also to Ed Stainless, two things, first I am trying to look at the demagnetization curves as you suggested, but the one I found was basically illegible.
Second I'm assuming you know something about stainless steel, what grades of S.S. are basically "non-magnetic"?

Thanks for helping out a "newbie" I've learned a lot from you guys.

-Todd

### RE: Field strength vs. gap between poles

The correct answer is 0.96T.  The magnet lengths add.  Think of a magnetic circuit this way.  The magnets are like batteries, their "Voltages" are in series (lengths are in series).  The gap is the "load" (magnetic resistance). The iron connecting the magnets is the "wiring" (it is sized so its "resistance" is not significant).  The magnet area is similar to the physical size of the "battery" (bigger batteries can source more current, i.e., more magnetic flux).

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