# Magnetic B Field Equation Due To Multi-Layer Solenoid

• benofer90
In summary, there are multiple formulas available for calculating the magnetic field of a multi-layer solenoid with a core. One option is to use Biot-Savart, but there may be some difficulties with the field not being homogenous and the strongest point not being at the center. Another option is to use a "work around" method found in a research paper. It is also possible to integrate a formula from an online resource with Biot-Savart. There is some uncertainty about the accuracy of the Biot-Savart formula provided and questions about calculating turns per unit length and the radius of the core.
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
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

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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.

( 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.

( 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:

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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 .

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

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

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## 1. What is the equation for the magnetic field due to a multi-layer solenoid?

The equation for the magnetic field (B) due to a multi-layer solenoid can be expressed as B = μ0 * N * I, where μ0 is the permeability of free space, N is the number of turns in the solenoid, and I is the current flowing through the solenoid.

## 2. How does the number of layers in a solenoid affect the magnetic field?

The number of layers in a solenoid does not directly affect the magnetic field. The magnetic field is primarily determined by the number of turns in the solenoid and the current flowing through it. However, a larger number of layers may result in a stronger magnetic field due to the increased number of turns and current.

## 3. How does the current flowing through a solenoid affect the magnetic field?

The magnetic field is directly proportional to the current flowing through a solenoid. This means that as the current increases, the magnetic field also increases. Similarly, if the current decreases, the magnetic field will also decrease.

## 4. How does the permeability of free space affect the magnetic field in a solenoid?

The permeability of free space, denoted by μ0, is a constant that represents the ability of a material to support the formation of a magnetic field. A higher permeability will result in a stronger magnetic field, while a lower permeability will result in a weaker magnetic field.

## 5. Is the magnetic field inside a multi-layer solenoid uniform?

No, the magnetic field inside a multi-layer solenoid is not uniform. The strength of the magnetic field varies along the length of the solenoid, with the strongest field being at the center and gradually decreasing towards the ends of the solenoid.

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