Calculation of the interaction between a 0 V potential

Flux
www.cedrat.com
Example
Creation
date
Calculation of the interaction between a 0V potential
sphere and a point electric charge
2009
Author : Pascal Ferran - Université Claude Bernard Lyon
Ref : FLU2_ES_ELE_01
Program
Dimension
Version
Physics
Application
Work
Flux
2D - axi
10.3
Electric
Static
Electric
FRAMEWORK
Presentation
General remarks
Analysis of the force induced by an empty sphere with a 0V potential on a point
charge containing N elementary charges.
This study underlines the electrostatic force existing between 2 elements.
Objective
Exploitation of the value of the electrostatic force induced by the sphere on a point
charge.
The parameters which can vary are :
The sphere radius (R_SPHERE)
The distance (DIST_A) between the sphere centre and the punctual charge
The number of elementary charges (N) contained in the point charge
Theoretical
reminders
Analytical calculation of the attractive force induced by the sphere on the point
charge :
F
R _ SPHERE  DIST _ A
1
 N ²  q² 
4 0
( DIST _ A²  R _ SPHERE²)²
Property
Illustration
-
Point charge value : N x q, with q = 1.6 E19 C and rated N = 20
-
Rated distance (DIST_A) between the
sphere centre and the point charge = 0.8
mm
-
Rated radius of the sphere :
= 0.3 mm
-
Relative permittivity of vacuum:
0
= 8.85 E-12 F/m
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]
R_SPHERE
FRAMEWORK
Flux
Some results…
Calculation of the force between the sphere and the punctual charge
Analytical Results
Flux result for the specified distance
1,2E-18
R_SPHERE :
DIST_A :
N:
F:
1E-18
Force (N)
8E-19
4,00E-4 m
8,00E-4 m
20
1,28E-19 N
6E-19
4E-19
2E-19
0
5,50E-04
6,00E-04
6,50E-04
7,00E-04
7,50E-04
8,00E-04
8,50E-04
9,00E-04
9,50E-04
1,00E-03
1,05E-03
Distance sphere centre - point : DIST_A (m)
Force value in function of the distance DIST_A
(other parameters are rated)
To go further…
-
PAGE 2
Replace the point region by a second sphere and vice-versa
Study the distribution of the electric field
Calculate the force between the 2 armatures of a capacity…
Calcul de l'interaction entre une sphère au potentiel 0 V et une charge électrique ponctuelle
Flux
MODEL IN FLUX
MODEL IN FLUX
Domain
Dimension
2D
Depth
Axi
« infinite » box
Length unit
mm
Angle unit
Degrees
Dimensions
Disk
Rint : 2 mm
Periodicity
-
Symmetry
Characteristics
Repetition number
Offset angle:
symetryYaxis_1 :
No active physical symmetry
Rext : 3 mm
1 symmetry
Even/odd periodicity
Physical application
Electrostatic
Property
Electric potential at infinite: 0 V
Geométry / mesh
Full model in the FLUX environment
Mesh
2nd order type
Mesh
Number of nodes
3724
Entry parameters
Name
R_SPHERE
Type
Geometrical
DIST_A
Geometrical
N
Physical
Description
Sphere radius
Distance between the sphere
centre and the point charge
Number of elementary charges
considered
Calcul de l'interaction entre une sphère au potentiel 0 V et une charge électrique ponctuelle
Rated value
0.3 mm
0.8 mm
1
PAGE 3
MODEL IN FLUX
Flux
Material base
NOM
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
AIR
Surface region
Air or vacuum
region
-
INFINITE
Surface region
Air or vacuum
region
-
POINT
Punctual
Region with charge
given by its total value
-
SPHERE
Line region
Stiff electric
potential
-
-
-
-
-
Electrical characteristics
-
-
Qtot = N x 1.6 E-19 C
0V
Current source
-
-
-
-
Thermal characteristics
-
-
-
-
Potential thermal source
-
-
-
-
PAGE 4
Calcul de l'interaction entre une sphère au potentiel 0 V et une charge électrique ponctuelle
Type
Associated material
Mechanical set
Component associated
circuit
Flux
MODEL IN FLUX
Mecanical set
Type
Characteristics
Miscellaneous
Mobile part :
Type of kinematics
Internal characteristics:
External characteristics :
Mechanical stops
Electric circuit
Component
Type
Characteristics
Associated Region
Electric scheme
Resolution parameters
Type of solver
Linear systems
Automatically
chosen
Parameters
Precision
Type of solver
Non linear systems
Newton Raphson
Automatically defined
Max. number
of itérations
0.0001
Method of calculation of the
relaxation coefficient
100
Authomatically specified
method
Thermal coupling
Advanced characteristics
Resolution
Scenario
Name of
parameter
Type of
configuration
Variation
method
Variation scale
Selection of the
steps
REFERENCEVALUES
-
-
-
-
-
Resolution time
1 second
Operating system
Windows XP 32 bits
Calcul de l'interaction entre une sphère au potentiel 0 V et une charge électrique ponctuelle
PAGE 5
ANNEX
Flux
ANNEX
Theoretical reminders
Calculation of the
force
General electrostatic equation :
  V   
Calculation of the attractive force exerted by the sphere on the point charge :
F
Notation and
symbols
1
4    0
symbol
 N ²  q² 
R _ SPHERE  DIST _ A
( DIST _ A²  R _ SPHERE ²)²
Description
Force exerted by the sphere on the
point charge
Absolute permittivity of vacuum
12
0
F
0
  8.85E
DIST_A
R_SPHERE
N
q
Distance between the sphere centre
and the point charge
Sphere radius
Number of elementary charges
constituting the point charge
Elementary charge
19
q  1.6 E
unit
N
F/m
m
m
C
Numerical applications
Calculation of
the force F for a
given point
Let’s calculate the value of the attractive force exerted by the sphere on the point
charge while the parameters are the following :
- Number of elementary charges constituting the point charge: N = 20
- Distance between the sphere centre and the point charge: DIST_A = 0.8 mm
- Rated radius of the sphere: R_SPHERE = 0.3 mm
F
1
4    0
 N ²  q² 
R _ SPHERE  DIST _ A
( DIST _ A²  R _ SPHERE²)²
0.3 0.8 10 6
1
2
19 2
F
 20  (1.6 10 ) 
4    8.85  10 12
(0.8  0.3) 2 10 6
F  7.30  10 20 N
PAGE 6
Calcul de l'interaction entre une sphère au potentiel 0 V et une charge électrique ponctuelle