Flux
Creation
date
Example
2009
Magnetic induction B created by a spire
www.cedrat.com
Author : Pascal Ferran - Université Claude Bernard Lyon
Ref. FLU2_MS_MAG_02
Program
Dimension
Version
Physics
Application
Work area
Flux
2D - axi
10.3
Magnetic
Static
Magnetic
FRAMEWORK
Presentation
General remarks
Study of the magnetic induction field radiated by a spire.
This example shows how to estimate the impact of the field radiated by a spire on its
environment (EMC type application).
Objective
Use of the magnetic induction B at a point M (x,0) located on the X-axis.
The x value will be between 0 and 25 mm.
Use of the magnetic induction B variation at a point N (0, y) located on the Y-axis.
The parameters the user can change are:
The current (I) injected in the spire
The radius R of the spire
Theoretical
reminders
Analytical computation of the B variation at a point N (0, y) located at a distance y of
the spire centre.
B 
µ0  I  sin 3 ( ) µ0  I
R2


2 R
2
( y 2  R 2 )3
Properties
Illustration
-
Copper conductor diameter : 1 mm
-
Spire rated radius : R = 10 mm
-
Rated injected current: I = 10 A
Main characteristics
CEDRAT S.A. 15, Chemin de Malacher Inovallée – 38246 MEYLAN Cedex (France) – Tél : +33 (0)4 76 90 50 45 – Email : [email protected]
FRAMEWORK
Flux
Some results …
Distribution of the magnetic flux surface density (B in Tesla)
Magnetic induction along the X-axis
PAGE 2
Magnetic induction B created by a spire
Flux
FRAMEWORK
Magnetic induction along the spire axis (Y-axis)
To go further …
-
Study of the magnetic field created by multiple spires (solenoid)
Study of a device with spires and magnetic core …
Magnetic induction B created by a spire
PAGE 3
MODEL IN FLUX
Flux
MODEL IN FLUX
Domain
Dimension
2D
Depth
axi
Infinite Box
Length unit.
mm
Angle unit.
degrees
Size
Periodicity
Symmetry
Characteristics
Repetition number :
Disk
In. radius : 40
Out. Radius : 50
1 symmetry
SymetryYaxis_1
Symmetry on the Y-axis – H tangent
Offset angle :
Even/odd periodicity
Application
Magneto static
Properties
Geometry / Mesh
Full model in the FLUX environment
Mesh
2nd order type
Mesh
Number of nodes
4192
Input Parameters
Name
Type
Description
Rated value
R
I
Geometrical
Physical
Spire radius
Electric current
10 mm
10 A
PAGE 4
Magnetic induction B created by a spire
Flux
MODEL IN FLUX
Material Base
NAME
B(H) model
Magnetic property
J(H) model
Electrical property
D(E) model
Dielectric property
K(T) model
K(T) characteristics
RCP(T) model
RCP(T) characteristics
Regions
NAME
Nature
Type
Material
Mechanical Set
Corresponding circuit
component
AIR
Surface density
Air region or vacuum
-
CONDUCTOR
Surface density
Coil conductor type region
-
INFINITE
Surface density
Air region or vacuum
-
-
COILCONDUCTOR
-
Electrical characteristics
-
1 spire
-
Current source
-
-
-
Thermal characteristics
-
-
-
Possible thermal source
-
-
-
Magnetic induction B created by a spire
PAGE 5
MODEL IN FLUX
Flux
Mechanical Set
Fixed part :
Compressible part :
Type
Characteristics
Miscellaneous
Mobile part :
Type of kinematics
Internal characteristics:
External characteristics :
Mechanical stops
Electrical circuit
Component
Type
Characteristics
Associated Region
COILCONDUCTOR
Coil conductor
Stiff current (A) : I
CONDUCTOR
Electric scheme
Solving process options
Type of linear system solver
Type of non-linear system
solver
Automatically
chosen
Parameters
Precision
Newton Raphson
Automatically defined
0.0001
Nb iterations
Method for computing the
relaxation factor
100
Automatically determined
method
Thermal coupling
Advanced characteristics
Solving
Scenario
Name of
parameter
Controllable
parameter
Variation
method
Interval definition
Step selection
REFERENCEVALUES
-
-
-
-
-
Duration of the solving
PAGE 6
1 second
Operating System
Windows XP 32 bits
Magnetic induction B created by a spire
Flux
ANNEX
ANNEX
Theoretical reminders
Computation of
the magnetic
induction
The magnetic induction at a point N (0, y) located along the Y-axis can be computed
by using:
  
 H  J
Maxwell equation :
Biot & Savart Law on Y-axis :
dB 
0 I
dl
sin( )
4 ( y ²  R ²)
By integrating B we get :
B
µ0 .I    R
 sin( )
2
2 ( y  R ²)
µ0  I  sin 3 ( ) µ0  I
R2
B


2 R
2
( y 2  R 2 )3
Notation and
symbols
Symbol
B
H
Description
Magnetic induction field
Magnetic field
Absolute permeability of vacuum
µo
µ0  4    10 7
J
I
R
y
Current Surface density
Current injected in the spire
Spire radius
Distance on Y-axis
unit
T
A/m
H/m
A/m²
A
m
m
Numerical applications
Computation of B
in the spire
centre
-
Spire radius R = 10 mm
Current I = 10 A
- Magnetic induction in the spire centre (y = 0) :
µ0  I
1 4   10 7 10
1
B 


  3  2 mT
2
R
2
10
Computation of B
at infinity
Computation of the magnetic induction at a point N (0, y) distant from the spire
centre:
lim B  lim
r 
Magnetic induction B created by a spire
r 
0  I
0
2  r
PAGE 7