Q-learning: Difference between revisions

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The Q-learning equation previously was *wrong* There are two ways to represent it and what was present was some incorrect hybrid of the two. I have corrected it. See http://webdocs.cs.ualberta.ca/~sutton/book/ebook/node65.html if you wish to validate.
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[[Image:VFPt maxwell coil.svg|right|thumb|300px|Magnetic field around a Maxwell coil]]
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<!-- Unsourced image removed: [[Image:Maxwell_Coils.png|right|thumb|222px|Maxwell coil layout in cylindrical coordinates.]] -->
A '''Maxwell coil''' is a device for producing a large volume of almost constant (or constant-gradient) [[magnetic field]]. It is named in honour of the Scottish physicist [[James Clerk Maxwell]].


A Maxwell coil is an improvement of a [[Helmholtz coil]]: in operation it provides an even more uniform magnetic field (than a Helmholtz coil), but at the expense of more material and complexity.
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==Description==
 
A constant-field Maxwell [[coil]] set consists of three coils oriented on the surface of a virtual sphere.<ref>Garrett, Milan Wayne, Journal of Applied Physics, 38(6), pp2563-2586</ref> <br>According to Maxwell's original 1873 design:<ref>{{cite book |last=Clerk-Maxwell |first=James |title=Treatise on Electricity and Magnetism |year=1873 |publisher=The Clarendon Press |location=Oxford |isbn=0-486-60636-8 }} Page 319.</ref> <br> each of the outer coils should be  of radius <math>\sqrt{\frac{4}{7}}R </math>,  and distance <math>\sqrt{\frac{3}{7}}R</math>  from the plane of <br> the central coil  of radius <math>R</math>. <br>The number of [[ampere-turn]]s of each of the smaller coils should equal exactly <math>\frac{49}{64}</math> of the middle coil. <br>This arrangement removes variations in magnetic field, up to its 6th-order derivative with respect to position, near the centre of the virtual sphere.
 
[[Image:Maxwellcoils.png]]
 
A gradient-field Maxwell [[coil]] is essentially the same geometry of the 3-coil configuration above, with the central coil removed to leave only the smaller two coils.<ref>R. Pascone, Manhattan College, T. Vullo and P.T. Cahill (1993) [http://ieeexplore.ieee.org/iel4/1093/8547/00701859.pdf Theoretical and experimental analysis of magnetic field gradients for MRI] from [[IEEE Explore]]</ref> If the current in one of the coils is reversed, a uniform-gradient magnetic field is produced near the centre of the two coils.
 
==References==
<references/>
 
==See also ==
*[[Magnetic field]]
*[[Helmholtz coil]]
*[[Halbach array]]
 
[[Category:Magnetic devices]]
[[Category:Electromagnetic coils]]

Revision as of 15:51, 26 February 2014

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