Re: Answers

>>From brzozoww-at-rchland.VNET.IBM.COM Tue Feb 27 13:18 MST 1996
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>Date: Tue, 27 Feb 1996 14:22:39 -0500 (EDT)
>From: Wesley Brzozowski <brzozoww-at-rchland.VNET.IBM.COM>
>To: tesla-at-grendel.objinc-dot-com
>Subject:  Answers 
> knagel-at-cnct-dot-com (Keith Nagel) writes; 
>> Joe Duszynski asks "Whats the inductance of a spherical inductor" 
>> L = (2*PI)/9  * mu0 * a * n,2 
>> where mu0 is the free space permeability, a is the radius of sphere, and n 
>> is turns. 
>That's interesting to know. I've seen some of these in antique radio equipment 
>(ticker coils, perhaps?) If some of the antique radio buffs here know
>for sure, 
>it would be fun to find out. 
>> Now, perhaps you can tell me why you need this? These coils have some 
>> interesting 
>> properties; for one, the H field inside has !no! curl. Weird, huh? And 
>> before the 
>> flames start, nothing in Maxwells equation prevents this. The field is still 
>> a dipole.   
>I don't think anyone here need flame you on that; curl-free fields aren't 
>impossible, they're just unusual; particularly where a magnetic field is 
>concerned. One quick example of a curl-free field would be in an area where 
>the field lines were parallel and all had the same magnitude. Wether or not 
>that's the case in the spherical inductor would take some work, so I'll  
>just take your word for it. Thanks for an interesting bit of info. 
>Wes B. 
Hello spherical coilers!
        A good example of a spherical inductor is the main superconducting
magnet in a magnetic resonance imager. Typically, four to six coils of
varying diameter are placed in an approximately spherical position.  The
picture below shows four coils, where the "[  ]" symbol is where the wire is
wrapped on individual cylindrical coil forms.

                    [  ]   [  ]
               [  ]              [  ]

         patient lies on table here
--------------------------------------------------  side view

               [  ]              [  ]
                    [  ]    [  ]

The magnetic field inside the sphere is uniform to within a fraction of a
part per million over a sphere of radius 20 cm.  The coils operate with
about 180 amperes current circulating in them continuously, supercooled by
liquid helium.
        You can make a spherical inductor simply by wrapping some stiff wire
using equal turns spacing on an inflated ball, and then deflating and
removing the ball.  Even 10 turns on a beach ball makes a remarkably uniform
field.  The geometry would probably not make a very good helical resonator,
Mark S. Rzeszotarski, Ph.D.