Magnetic B Field Equation Due To Multi-Layer Solenoid

Click For Summary
SUMMARY

The discussion focuses on the Magnetic B Field Equation for a multi-layer solenoid with a core, specifically addressing the complexities of calculating the magnetic field using the Biot-Savart law. Key parameters include coil length (ℓA), radial dimension of winding (xR), winding pitch (pA, pR), and the number of turns per layer (NT=6) and layers (NL=5). The participants emphasize the non-homogeneous nature of the magnetic field within the core and suggest numerical calculations for accurate results. They also reference various resources, including a research paper on multilayer gradient coil design.

PREREQUISITES
  • Understanding of Biot-Savart law for magnetic field calculations
  • Familiarity with solenoid design parameters (e.g., coil length, winding pitch)
  • Basic knowledge of electromagnetic theory and permeability
  • Experience with numerical programming for magnetic field simulations
NEXT STEPS
  • Research "Biot-Savart law applications in multilayer solenoids"
  • Study "Magnetic field calculations for multi-layer solenoids" in academic journals
  • Explore "Numerical methods for electromagnetic field simulations" using software tools
  • Review "Gradient coil design principles" in the context of MRI technology
USEFUL FOR

Electrical engineers, physicists, and researchers involved in electromagnetic design, particularly those working with solenoids and magnetic field simulations.

benofer90
Messages
64
Reaction score
1
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:
Physics news on Phys.org
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" ).
 
Last edited:
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
 
Last edited by a moderator:
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:

Similar threads

Graduate Biot Savart Law with Different Magnetic Permeabilities
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Calculating the magnetic field in this seemingly simple case?
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Calculating magnetic field for a micro solenoid
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Solenoid Magnetic Field Testing
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Calculating the magnetic field in solenoid
  • · Replies 2 ·
Replies
2
Views
4K
Graduate Magnetic field due to a solenoid.
  • · Replies 4 ·
Replies
4
Views
2K
Graduate How does the magnetic field strength decay(radially) inside a solenoid coil?
  • · Replies 11 ·
Replies
11
Views
8K
Why is magnetic field half at the sides of a solenoid?
  • · Replies 11 ·
Replies
11
Views
3K
Graduate Calculating the magnetic field of a closed magnetic circuit
  • · Replies 1 ·
Replies
1
Views
2K
{ help } Calculating the B-field at the center of a solenoid
  • · Replies 1 ·
Replies
1
Views
2K