Magnetic B Field Equation Due To Multi-Layer Solenoid

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Discussion Overview

The discussion revolves around the Magnetic B Field Equation for a multi-layer solenoid with a core. Participants explore various formulas, the implications of core material properties, and the challenges of calculating the magnetic field in non-homogeneous regions within the solenoid.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants mention the basic equation B = Niμ/ℓA but seek more complex formulations for multi-layer configurations.
  • There is a concern about the non-homogeneous nature of the magnetic field within the core, leading to questions about where to measure the field.
  • Biot-Savart law is suggested as a potential method for numerical calculations, with recommendations to start with simpler configurations.
  • One participant questions whether the magnetic field is strongest at the center of the solenoid, suggesting it may be stronger near the windings due to shorter circulation paths.
  • Participants express uncertainty about the relevance of the radius of each loop in the context of the magnetic field calculations.
  • There is a request for examples of using Biot-Savart in multilayer formulas, indicating a desire for clarity on integrating various resources.

Areas of Agreement / Disagreement

Participants express differing views on the best approach to calculate the magnetic field, with some favoring Biot-Savart and others suggesting alternative methods. The discussion remains unresolved regarding the optimal formula and the implications of core geometry on the magnetic field strength.

Contextual Notes

Participants highlight limitations in existing formulas, particularly concerning the number of layers and the specific geometry of the solenoid. There are unresolved questions about the assumptions underlying the calculations and the dependence on specific parameters.

benofer90
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Anyone knows the Magnetic B Field Equation Due To Multi-Layer Solenoid(with a core) ?

where:
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
 
Last edited by a moderator:
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benofer90 said:
Anyone knows the Magnetic B Field Equation Due To Multi-Layer Solenoid(with a core) ?
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 ).
 
Hesch said:
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 ).

Thank you Hesch,

I did google finding this one ... what do you think about "B ending" ?
http://physics.stackexchange.com/questions/95725/magnetic-field-of-a-solenoid-at-the-poles
 
benofer90 said:
what do you think about "B ending" ?
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" ).
 
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Hesch said:
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" ).

I know that is why I am struggling to find something that match . also does it matter the radius of each loop ?
 
benofer90 said:
I know that is why I am struggling to find something that match . also does it matter the radius of each loop ?

any thoughts ?
 
benofer90 said:
any thoughts ?
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
 
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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 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:
Hesch said:
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

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:

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