ElectricFluxDensityValue
ElectricFluxDensityValue[pred,vars,pars]
represents an electric flux density boundary condition for PDEs with predicate pred indicating where it applies, with model variables vars and global parameters pars.
ElectricFluxDensityValue[pred,vars,pars,lkey]
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)
Applications (2)
Model a parallel electric field with an electric flux density boundary. Set up the electrostatic model variables :
Specify electrostatic model parameter relative permittivity :
Set up a ground potential at the right boundary of the box:
Set up an inward electric flux density boundary condition at the left boundary of the box:
Compute the electric field intensity E:
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 :
Specify electrostatic model parameter relative permittivity :
Set up a positive surface charge density at the upper boundary:
Text
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.
APA
Wolfram Language. (2024). ElectricFluxDensityValue. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ElectricFluxDensityValue.html