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Magnetic B Field Equation Due To Multi-Layer Solenoid

  1. Aug 8, 2015 #1
    Anyone knows the Magnetic B Field Equation Due To Multi-Layer Solenoid(with a core) ?

    Core Material "μ" is of radius R1(NOT shown in the below drawing)
    i - Current
    μ - Permeability (of Core Material)

    All length, diameter and pitch measurements are from centre to centre of the conductors as shown.
    Definition of Parameters:
    ℓA - Coil Length
    xR - Radial dimension of winding (winding depth)
    pA - Winding pitch along axis
    pR - Radial winding pitch
    Do - Outside Diameter of Coil
    Di - Inside Diameter of Coild - Diameter of conductor (excluding insulation)
    di - Outside diameter of conductor including insulation
    NT - Number of turns per layer (NT=6 in the diagram)
    NL - Number of winding layers (NL=5 in the diagram)
    (Note that uppercase D parameters refer to overall coil diameters while lowercase d parameters refer to conductor diameters.)

    I know some basic part of the equation: B= Niμ/ℓA

    http://electronbunker.ca/InductanceCalcML_files/droppedImage.jpg [Broken]
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Aug 10, 2015 #2


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    There are some different formulas to be googled ( more/less complicated → less/more adapted ).

    There is a problem concerning: Where in the core? because the field is not homogenious.

    But Biot-Savart should work, numerically calculated. So some programming, then wait 15 minutes for the result to be calculated. :smile:

    ( At first, test the program with only one layer and a limited number of turns ).
  4. Aug 10, 2015 #3
    Thank you Hesch,

    I did google finding this one ... what do you think about "B ending" ?
  5. Aug 10, 2015 #4


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    I have no comments to that. I think adapted formulas are used, that "fit" whatever shape of a solenoid.

    Also I'm not sure that the B-field is strongest at the center of a solenoid. Maybe very close to one the windings it will be stronger, because the length of a circulation path is very short, following the surface of a wire. ( Regarding Amperes law ).

    As I read your linked, there is only 1 layer in the formula. ( Only 1 "R" ).
    Last edited: Aug 10, 2015
  6. Aug 13, 2015 #5
    I know that is why I am struggling to find something that match . also does it matter the radius of each loop ?
  7. Aug 16, 2015 #6
    any thoughts ?
  8. Aug 16, 2015 #7


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    Yes, yes: If you really don't want to use Biot-Savart, there is a "work around" here:

    http://www.researchgate.net/publication/222492899_Multilayer_Gradient_Coil_Design [Broken]
    Last edited by a moderator: May 7, 2017
  9. Aug 17, 2015 #8
    I do want to use Biot-Savart but in multilayer formula. any idea where i can find an example for one? the http://www.researchgate.net/publication/222492899_Multilayer_Gradient_Coil_Design [Broken] formula is not so clear to me . thanks

    If we can integrate this : http://info.ee.surrey.ac.uk/Workshop/advice/coils/air/area.xhtml
    with Biot-Savart that would be great .
    Last edited by a moderator: May 7, 2017
  10. Aug 18, 2015 #9
    also can i ask if the B end at the first link i provided of Biot-Savart, is actually Biot-Savart?
    How do i calculate N = turns per unit length
    and R is of the total Coil ? what about the core ?

    thank you
    Last edited by a moderator: May 7, 2017
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