Изображение:Hall effect.png

Shows the Hall effect for different directions of electric current and magnetic field.

Legend:

1. Electrons (not conventional current!)
2. Hall element, or Hall sensor
3. Magnets
4. Magnetic field
5. Power source

In drawing "A", the Hall element takes on a negative charge at the top edge (symbolised by the blue color) and positive at the lower edge (red color). In "B" and "C", either the electric current or the magnetic field is reversed, causing the polarization to reverse. Reversing both current and magnetic field (drawing "D") causes the Hall element to again assume a negative charge at the upper edge.

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This image was selected as a picture of the day for October 19, 2005. It was captioned as followed: English: Hall effect Deutsch: Illustration des Hall-Effekts Français : L'effet Hall illustré Español: Ilustración del efecto Hall Aragonés: Efeuto Hall Česky: Hallův jev Deutsch: Illustration des Hall-Effekts English: Hall effect Español: Ilustración del efecto Hall Eesti: Hall'i effekti illustratsioon Français : L'effet Hall illustré Gaeilge: Iarmhairt Hall Galego: Efeto Hall. 日本語: ホール効果 Latina: Nederlands: Illustratie nl:Hall-effect Polski: Efekt Halla Português: Diagrama do efeito Hall Русский: Эффект Холла Slovenščina: Hallov pojav ไทย: ปรากฏการณ์ฮอลล์ zh-hans: 哈尔效应示意图

I, the author of this work, hereby publish it under the following license: Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License". العربية | Česky | Deutsch | English | Español | Français | Italiano | 日本語 | 한국어 | Nederlands | Polski | Português | Slovenčina | Svenska | עברית +/-

Rendered using POV-Ray (see http://www.povray.org). The scene description "code" shown below supports rendering all of the four "situations" portrayed in the image - see the comment given in the code. The four images were subsequently combined, and the numbers and letters added, in a graphics software package.

POV-Ray "code" for rendering all four parts of the illustration:

 /*
 ====================================================
 The Hall effect in metal under various circumstances
 ----------------------------------------------------
 Created by Søren Peo Pedersen - see my user page at
 http://da.wikipedia.org/wiki/Bruger:Peo
 ====================================================
 */
 
 #declare NorthAtLeft=no; // Orientation of magnetic field:
 // Use "yes" for north pole to the left, and south pole to the right
 // Use "no" for north pole to the right, and south pole to the left
 
 #declare PlusTowardsViewer=yes;  // Direction of current:
 // Use "yes" to have the positive pole at the ends of battery and Hall sensor nearest to viewer
 // Use "no" to have the negative pole at the ends of battery and Hall sensor nearest to viewer
 
 #declare PositiveCharge=no; // Polarity (color) of charge carriers in the circuit:
 // Use "yes" for orangeish colored charge carriers in wires and Hall sensor
 // Use "no" for light blue colored charge carriers in wires and Hall sensor
 
 #declare HallUpwards=yes; // Direction of sideways force upon charge carriers:
 // Use "yes" to have the charge carriers "bend upwards" inside Hall element
 // Use "no" to have the charge carriers "bend downwards" inside Hall element
 
 #declare NegativeEdgeUp=yes;  // Electrical polarization of Hall element (indicated by color):
 // Use "yes" to have bluish color at top of Hall element, indicating negative charge here
 // Use "no" to have reddish color at top of Hall element, indicating positive charge here
 
 #declare MagnetFont="arialbd.ttf" // Font for the "N" and "S" nomenclature on magnets
 
 // -----------------------------------------------------------------------------------------
 
 #declare txtNeutralElement=texture {  // Texture for electrically neutral parts of Hall element
   pigment {color rgbft <.5,.5,.5,1,0>}
   finish {
     reflection rgb .5
     phong 1
     metallic
     }
   }
   
 #declare txtNegativeElement=texture { // Texture for negatively charged parts of Hall element
   pigment {color rgbft <.1,.3,.9,1,0>}
   finish {
     reflection rgb <.1,.3,.9>
     phong 1
     metallic
     }
   }
   
 #declare txtPositiveElement=texture { // Texture for positively charged parts of Hall element
   pigment {color rgbft <.9,.3,.1,1,0>}
   finish {
     reflection rgb <.9,.3,.1>
     phong 1
     metallic
     }
   }
 
 #declare txtPolarisedElement=texture {  // Texture for polarized parts of the Hall element
   gradient y
   texture_map {
     [0 txtNegativeElement]
     [.5 txtNeutralElement]
     [1 txtPositiveElement]
     }
   translate <0,-.5,0>
   #if (NegativeEdgeUp)
     rotate <180,0,0>
   #end
   }
 
 #declare txtHallElement=texture { // Complete texture for the entire Hall element
   gradient z
   texture_map {
     [0 txtNeutralElement]
     [.5 txtPolarisedElement]
     [1 txtNeutralElement]
     }
   translate <0,0,-.5>
   scale 4
   }
 
 #declare WireTxt=texture {  // Texture for the wires connecting Hall element with power source
   pigment {color rgb .5}
   finish {
     reflection rgb .7
     phong 3
     metallic
     }
   }
 
 #declare Qtorus=intersection{   // 1/4 of a torus, for rounded "corner" on the wiring
   torus {1,.06 rotate <0,0,90>}
   box {-2,<2,0,0>}    
   }
 
 #declare PlusPgmt=pigment {   // Pigment for positive end of the battery (power source)
   object {
     merge {
       box {<-.3,0, .35>,<.3,1,.45>}
       box {<-.05,0, .1>,<.05,1,.7>}
       }
     pigment {color rgb <1,0,0>}
     pigment {color rgb 1}
     }
   }
 
 #declare MinusPgmt=pigment {  // Pigment for negative end of the battery (power source)
   object {        
     box {<-.3,0,-.55>,<.3,1,-.45>}
     pigment {color rgb <0,0,1>}
     pigment {color rgb 1}
     }
   }
 
 #declare PowerSource=union {  // Power source, symbolised by a battery
   merge {
     torus {.45,.05 rotate <90,0,0> translate <0,0,-.95>}
     cylinder {<0,0,-.95>,<0,0,.8>,.5}
     torus {.45,.05 rotate <90,0,0> translate <0,0, .8>}
     pigment {
       object {
         plane {<0,0,1>,0}
         pigment {PlusPgmt}
         pigment {MinusPgmt}
         }
       rotate <0,0,-35>
       }
     finish {ambient .4}
     }
   merge {
     torus {.35,.05 rotate <90,0,0> translate <0,0,-.95>}
     cylinder {<0,0,-1>,<0,0,-.9>,.35}
     torus {.35,.05 rotate <90,0,0> translate <0,0,.8>}
     cylinder {<0,0,.85>,<0,0,.8>,.35}
     difference {
       cylinder {<0,0,.85>,<0,0,.9>,.15}
       torus {.15,.05 rotate <90,0,0> translate <0,0,.9>}
       }
     cylinder {<0,0,.9>,<0,0,.95>,.1}
     torus {.05,.05 rotate <90,0,0> translate <0,0,.95>}
     cylinder {<0,0,.95>,<0,0,1>,.05}
     pigment {color rgb .5}
     finish {reflection rgb .9 phong 1 metallic}
     }
   }
 
 #macro txtChargeCarrier(Transparency) // Texture for charge carriers and their "motion blur tails"
 pigment {color rgbt <
   #if (PositiveCharge)
   1,.5,.2,Transparency
   #else
   .2,.5,1,Transparency
   #end
   >}
 finish {ambient .4}
 #end
 
 #declare FieldArrow=merge {   // Arrow indicating direction of magnetic field
   cylinder {<-2.5,0,0>,<2.3,0,0>,.003}
   cone {<2.3,0,0>,.05,<2.5,0,0>,0}
   pigment {color rgb 0}
   #if (NorthAtLeft)
   #else
   scale <-1,1,1>
   #end
   no_shadow
   no_reflection    
   }
 
 #declare StraightCharge=union {   // Charge carrier with straight "motion blur tail"
   sphere {0,.15 texture {txtChargeCarrier(0)}}
   cylinder {0,<0,0,.499>,.15 hollow
     texture {
       gradient z
       texture_map {
         [0 txtChargeCarrier(0)]
         [1 txtChargeCarrier(1)]
         }
       scale .5
       }        
     }
   no_shadow
   no_reflection
   }
 
 #declare CurvedCharge=union {   // Charge carrier with curved "motion blur tail"
   sphere {<0,-1,0>,.15 texture {txtChargeCarrier(0)}}
   difference {
     torus {1,.15 rotate <0,0,90>}
     plane {<0,0,1>,0}
     plane {<0,0,-1>,0 rotate <-29.99,0,0>}
     hollow
     texture {
       radial
       texture_map {
         [0 txtChargeCarrier(.3)]
         [1 txtChargeCarrier(1)]
         }
       frequency 12
       rotate <0,0,90>
       }
     }
   no_shadow
   no_reflection
   }
 
   // The scenario:  
   box {<-.16,-1,-2>,<.16,1,2>   // The hall element
     texture {txtHallElement}        
     no_shadow
     }
   
   merge { // Wiring with travelling charge carriers
     // Wiring on the side towards the viewer:
     cylinder {<0,0,-2>,<0,0,-3>,.06}
     #object {Qtorus rotate <90,0,0> translate <0,-1,-3>}
     cylinder {<0,-1,-4>,<0,-2,-4>,.06}
     #object {Qtorus translate <0,-2,-3>}
     cylinder {<0,-3,-3>,<0,-3,-1>,.06}
     // Wiring on the side facing away from the viewer:
     cylinder {<0,-3, 1>,<0,-3, 3>,.06}
     #object {Qtorus rotate <-90,0,0> translate <0,-2,3>}
     cylinder {<0,-1, 4>,<0,-2, 4>,.06}
     #object {Qtorus rotate <180,0,0> translate <0,-1,3>}
     cylinder {<0,0, 2>,<0,0, 3>,.06}
     texture {WireTxt}
     }
 
   union { // Charge carriers:
     // Charge carriers on the side towards the viewer:
     #object {StraightCharge translate <0,-3,-2.7>}
     #object {CurvedCharge rotate <30,0,0> translate <0,-2,-3>}
     #object {CurvedCharge rotate <90,0,0> translate <0,-2,-3>}
     #object {StraightCharge rotate <90,0,0> translate <0,-1,-4>}
     #object {StraightCharge rotate <90,0,0> translate <0,-1,-4>}
     #object {CurvedCharge rotate <150,0,0> translate <0,-1,-3>}
     #object {StraightCharge rotate <180,0,0> translate <0,0,-2.5>}
     // Charge carriers inside Hall element:
     #if (HallUpwards)
       #object {CurvedCharge rotate <195,0,0> translate <0,-.3,0>}
       #object {CurvedCharge rotate <30,180,0> translate <0,1.15,-1.5>}
       #object {CurvedCharge rotate <0,180,0> translate <0,1.15,1.5>}
     #else
       #object {CurvedCharge rotate <210,0,0> translate <0,-1,-1.5>}
       #object {CurvedCharge rotate <15,180,0> translate <0,.3,0>}
       #object {CurvedCharge rotate <180,0,0> translate <0,-1,1.5>}
     #end
     // Charge carriers on the side facing away from the viewer:
     #object {StraightCharge rotate <180,0,0> translate <0,0,3>}
     #object {CurvedCharge rotate <270,0,0> translate <0,-1,3>}
     #object {StraightCharge rotate <270,0,0> translate <0,-2,4>}
     #object {CurvedCharge rotate <330,0,0> translate <0,-2,3>}
     #object {StraightCharge translate <0,-3,2.3>}
     #if (PlusTowardsViewer)
       scale <1,1,-1>
     #end
     }
       
   #object {PowerSource  // The battery symbolising the power source of the circuit
       #if (PlusTowardsViewer) scale <1,1,-1> #end
       scale 2
       translate <0,-3,0>
       }
   
   #union {    // Pair of magnets
     // The magnet at the left-hand side of the image:
     box {<-15,-1,-1>,<-3,1,1>
       pigment {
         object {
           text {ttf MagnetFont
             #if (NorthAtLeft) "N" #else "S" #end
             ,3,0
             scale 2
             translate <-4.3,-.7,-1.5>
             }
           #if (NorthAtLeft)
             color rgb <1,0,0>
             color rgb .85
           #else
             color rgb .85
             color rgb <1,0,0>
           #end
           }
         }
       finish {ambient .4}
       no_shadow
       no_reflection
       }
     // The magnet at the right-hand side of the image:
     box {<3,-1,-1>,<15,1,1>
       pigment {
         object {
           text {ttf MagnetFont
             #if (NorthAtLeft) "S" #else "N" #end
             ,3,0
             scale 2
             translate <3.2,-.7,-1.5>
             }
           #if (NorthAtLeft)
             color rgb .85
             color rgb <1,0,0>
           #else
             color rgb <1,0,0>
             color rgb .85
           #end
           }
         }
       finish {ambient .4}
       no_shadow
       no_reflection
       }
     }
 
 // 4 x 4 arrows to indicate the direction of the magnetic field:
 #local Ktal=-.75;
 #while (Ktal<1)
   #local Rtal=-.75;
   #while (Rtal<1)
     #object {FieldArrow translate <0,Rtal,Ktal>}
     #local Rtal=Rtal+.5;
   #end
   #local Ktal=Ktal+.5;
 #end
 
 // Point of view:
 camera {
     location <4,3,-5>
     look_at <.8,-1.3,0>
     }
 
 // Illumination:
 light_source {<20,10,-15> color rgb 1}
 light_source {<-10,20,10> color rgb 1}
 
 // Spotty surroundings outside viewfield to enhance reflective surfaces:
 #declare Spotty=pigment {
   marble
   color_map {
     [0 color rgb 0]
     [1 color rgb .8]
     }
   scale .1
   }
 
 sky_sphere {
   pigment {
     gradient z
     pigment_map {
       [0.00 Spotty]
       [0.88 Spotty]
       [0.88 color rgb 1]
       [1.00 color rgb 1]
       }
     translate -.5
     scale 2
     rotate <35,-32,0>
     }
   }