ElectricFluxDensityValue
✖
ElectricFluxDensityValue
represents an electric flux density boundary condition for PDEs with predicate pred indicating where it applies, with model variables vars and global parameters pars.
represents an electric flux density boundary condition with local parameters specified in pars[lkey].
Details



- ElectricFluxDensityValue specifies a Neumann boundary value for the ElectrostaticPDEComponent
- ElectricFluxDensityValue specifies a boundary condition for ElectrostaticPDEComponent and is used as part of the modeling equation:
- ElectricFluxDensityValue is typically used to model an electric flux density
field in units of [
] that enters or leaves a boundary.
- The flux is caused by a surface charge density
in units of [
] positioned at a boundary.
- A positive value denotes the inward electric flux, and a negative value denotes an outward flux.
- ElectricFluxDensityValue models an electric flux density
field normal to the boundary with dependent variable
in volts [
] and independent variables
in [
].
- Stationary variables vars are vars={Θ[x1,…,xn],{x1,…,xn}}.
- The polarized form of ElectrostaticPDEComponent with vacuum permittivity
in units of [
], polarization vector
in units of [
] and volume charge density
in units of [
] is given by:
- When specified at an outer boundary ElectricFluxDensityValue models:
is a surface charge density in units of [
] at an outer or interior boundary, and
is a surface electric flux density in units of [
].
- When specified at an interior boundary between two nonconducting materials with electric flux density fields
and
, ElectricFluxDensityValue models:
- Model parameters pars are specified as for ElectrostaticPDEComponent.
- The following additional model parameters pars can be given:
-
parameter default symbol "ElectricFluxDensity" - {0,...}
, bondary electric flux density in [
]
"BoundaryUnitNormal" Automatic "SurfaceChargeDensity" , surface charge density in [
]
- All model parameters may depend on the spatial variables
.
- To localize model parameters, a key lkey can be specified and values from association pars[lkey] are used for model parameters.
- ElectricFluxDensityValue evaluates to a NeumannValue.
- The boundary predicate pred can be specified as in NeumannValue.
- If the ElectricFluxDensityValue depends on parameters
that are specified in the association pars as …,keypi…,pivi,…], the parameters
are replaced with
.




Examples
open allclose allBasic Examples (3)Summary of the most common use cases
Set up an electric flux density boundary condition:

https://wolfram.com/xid/0dbjl13pdqimsb20oq-vw7olo

Set up a surface charge density at the boundary:

https://wolfram.com/xid/0dbjl13pdqimsb20oq-u9ksq

Set up a surface charge density at a boundary, for a 2D electrostatic model that has a thickness :

https://wolfram.com/xid/0dbjl13pdqimsb20oq-giqrx

Applications (2)Sample problems that can be solved with this function
Model a parallel electric field with an electric flux density boundary. Set up the electrostatic model variables :

https://wolfram.com/xid/0dbjl13pdqimsb20oq-l31rgn

https://wolfram.com/xid/0dbjl13pdqimsb20oq-mb3sl1
Specify electrostatic model parameter relative permittivity :

https://wolfram.com/xid/0dbjl13pdqimsb20oq-twb86
Set up a ground potential at the right boundary of the box:

https://wolfram.com/xid/0dbjl13pdqimsb20oq-lhua7
Set up an inward electric flux density boundary condition at the left boundary of the box:

https://wolfram.com/xid/0dbjl13pdqimsb20oq-bpt5u


https://wolfram.com/xid/0dbjl13pdqimsb20oq-hk3stc

https://wolfram.com/xid/0dbjl13pdqimsb20oq-vxinx8
Compute the electric field intensity E:

https://wolfram.com/xid/0dbjl13pdqimsb20oq-e9rgz6

https://wolfram.com/xid/0dbjl13pdqimsb20oq-dp1xps

Instead of specifying a voltage difference in a capacitor, one can also specify a surface charge density in one of the plates of the capacitor. Set up the electrostatic model variable :

https://wolfram.com/xid/0dbjl13pdqimsb20oq-inm3ug

https://wolfram.com/xid/0dbjl13pdqimsb20oq-fpjpub
Specify electrostatic model parameter relative permittivity :

https://wolfram.com/xid/0dbjl13pdqimsb20oq-k5a3d
Set up a positive surface charge density at the upper boundary:

https://wolfram.com/xid/0dbjl13pdqimsb20oq-b82vm3

Set up a ground potential at the lower boundary:

https://wolfram.com/xid/0dbjl13pdqimsb20oq-el3xag

https://wolfram.com/xid/0dbjl13pdqimsb20oq-bn35hn

https://wolfram.com/xid/0dbjl13pdqimsb20oq-cb7nna

https://wolfram.com/xid/0dbjl13pdqimsb20oq-kfnm0j

Wolfram Research (2024), ElectricFluxDensityValue, Wolfram Language function, https://reference.wolfram.com/language/ref/ElectricFluxDensityValue.html.
Text
Wolfram Research (2024), ElectricFluxDensityValue, Wolfram Language function, https://reference.wolfram.com/language/ref/ElectricFluxDensityValue.html.
Wolfram Research (2024), ElectricFluxDensityValue, Wolfram Language function, https://reference.wolfram.com/language/ref/ElectricFluxDensityValue.html.
CMS
Wolfram Language. 2024. "ElectricFluxDensityValue." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ElectricFluxDensityValue.html.
Wolfram Language. 2024. "ElectricFluxDensityValue." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ElectricFluxDensityValue.html.
APA
Wolfram Language. (2024). ElectricFluxDensityValue. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ElectricFluxDensityValue.html
Wolfram Language. (2024). ElectricFluxDensityValue. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ElectricFluxDensityValue.html
BibTeX
@misc{reference.wolfram_2025_electricfluxdensityvalue, author="Wolfram Research", title="{ElectricFluxDensityValue}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/ElectricFluxDensityValue.html}", note=[Accessed: 07-June-2025
]}
BibLaTeX
@online{reference.wolfram_2025_electricfluxdensityvalue, organization={Wolfram Research}, title={ElectricFluxDensityValue}, year={2024}, url={https://reference.wolfram.com/language/ref/ElectricFluxDensityValue.html}, note=[Accessed: 07-June-2025
]}