## PSN-L Email List Message

Subject: Re: Sensor magnet and coil design
From: Bobhelenmcclure@.......
Date: Sat, 7 Oct 2006 01:11:01 EDT

On Fri, 6 Oct 2006 06:18:14 EDT, ChrisAtUpw@.......  writes:
>   Now it is time to discuss what field strength you  get, and what
thickness
> of steel is required. Suppose for my example  using 6 mm thick magnets, I
use
> a gap of 6 mm. The resulting distance  between plates is 18 mm, 12 mm
filled
> with magnet, and 6 mm with air. I  call the ratio of total magnet thickness
to
> total plate separation the  filling factor. To a first approximation, the
gap
> field the coercive  force of the magnetic material multiplied by the
filling
> factor. In  this example, the coercive force is 12 KOe and the filling
factor
> is  2/3, so the gap field is 8 KOe. The accuracy of this estimate depends
on
> the magnet width compared to the gap size. If the gap becomes  appreciable
> compared to the width, you will get more fringing field and
less-than-expected
> gap field.

Can you run through the maths and  assumptions of this please?

Hi Chris,

I am assuming that the Nd magnet material is very hard  magnetically, and has
an incremental permeability almost the same as air. It can  be considered to
be an empty volume whose pole faces are coated uniformly  with magnetic
charges. Charges on one face are connected by lines of force to  opposite charges.
First consider a stack of magnets with infinitesimal gaps  between them. In
this case, opposite charges are adjacent, so all the lines  cross the gap to the
next magnet, and none travel back through the magnet to the  opposing poles at
the other end, and we get at the gap the flux of the short  circuit coercive
force. As we widen the gaps, more and more flux returns to the  opposing face
of each magnet instead of crossing the gap to the next magnet.  With this line
of reasoning, we are down to a flux of 50% when the gap spacing  equals the
magnet thickness, and so on.

The four pole magnet structure can be shown to be similar in field  pattern
to a repeating structure of magnets and gaps, so my conclusions rest on  the
validity of the assumption of a relative permeability of 1.0 for the  magnets.
If the incremental permeability is higher than 1, then the field will  fall
off faster with increasing gap spacing. The finite transverse dimensions of
the magnets is another reason for more rapid falloff.

--Bob

On Fri, 6 Oct 2006 06:18:14 EDT, ChrisAtUpw@.......=20 writes:
>   Now it is time to discuss what field strength yo= u=20 get, and what thickness
> of steel is required. Suppose for my exampl= e=20 using 6 mm thick magnets, I use
> a gap of 6 mm. The resulting distan= ce=20 between plates is 18 mm, 12 mm filled
> with magnet, and 6 mm with ai= r. I=20 call the ratio of total magnet thickness to
> total plate separation=20= the=20 filling factor. To a first approximation, the gap
> field the coerciv= e=20 force of the magnetic material multiplied by the filling
> factor. In= =20 this example, the coercive force is 12 KOe and the filling factor
> i= s=20 2/3, so the gap field is 8 KOe. The accuracy of this estimate depends on=20
> the magnet width compared to the gap size. If the gap becomes=20 appreciable
> compared to the width, you will get more fringing field= and=20 less-than-expected
> gap field.

Can you run through the maths and=20 assumptions of this please?

Hi Chris,

I am assuming that the Nd magnet material is very hard=20 magnetically, and has an incremental permeability almost the same as air. It= can=20 be considered to be an empty volume whose pole faces are coated uniform= ly=20 with magnetic charges. Charges on one face are connected by lines of force t= o=20 opposite charges. First consider a stack of magnets with infinitesimal gaps=20 between them. In this case, opposite charges are adjacent, so all the lines=20 cross the gap to the next magnet, and none travel back through the magnet to= the=20 opposing poles at the other end, and we get at the gap the flux of the short= =20 circuit coercive force. As we widen the gaps, more and more flux returns to=20= the=20 opposing face of each magnet instead of crossing the gap to the next magnet.= =20 With this line of reasoning, we are down to a flux of 50% when the gap spaci= ng=20 equals the magnet thickness, and so on.

The four pole magnet structure can be shown to be similar in fie= ld=20 pattern to a repeating structure of magnets and gaps, so my conclusions rest= on=20 the validity of the assumption of a relative permeability of 1.0 for the=20 magnets. If the incremental permeability is higher than 1, then the field wi= ll=20 fall off faster with increasing gap spacing. The finite transverse dimension= s of=20 the magnets is another reason for more rapid falloff.

--Bob

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