Magnetic B Field Equation Due To Multi-Layer Solenoid

[benofer90]

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

 

[Hesch]

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.

( At first, test the program with only one layer and a limited number of turns ).

 

[benofer90]

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.

( 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

 

[Hesch]

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" ).

 

[benofer90]

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]

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

any thoughts ?

 

[Hesch]

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

 

[benofer90]

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 .

 

[benofer90]

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