ElectricSymmetryValue
ElectricSymmetryValue[pred,vars,pars]
represents an electric symmetry boundary condition for PDEs with predicate pred indicating where it applies, with model variables vars and global parameters pars.
ElectricSymmetryValue[pred,vars,pars,lkey]
represents an electric symmetry boundary condition with local parameters specified in pars[lkey].
Details
- ElectricSymmetryValue specifies a symmetry boundary condition for ElectrostaticPDEComponent.
- ElectricSymmetryValue specifies a boundary condition for ElectrostaticPDEComponent and is used as part of the modeling equation:
- ElectricSymmetryValue is typically used to model a boundary with mirror symmetry along an axis.
- ElectricSymmetryValue models a boundary with mirror symmetry with dependent variable
, independent variables 
and time variable 
. - Stationary variables vars are vars={V[x1,…,xn],{x1,…,xn}}.
- The polarized form of ElectrostaticPDEComponent with vacuum permittivity
in units of [![TemplateBox[{InterpretationBox[, 1], {"F", , "/", , "m"}, farads per meter, {{(, "Farads", )}, /, {(, "Meters", )}}}, QuantityTF]](Files/ElectricSymmetryValue.en/7.png "TemplateBox[{InterpretationBox[, 1], {\"F\", , \"/\", , \"m\"}, farads per meter, {{(, \"Farads\", )}, /, {(, \"Meters\", )}}}, QuantityTF]")
], polarization vector 
in units of [![TemplateBox[{InterpretationBox[, 1], {"C", , "/", , {"m", ^, 2}}, coulombs per meter squared, {{(, "Coulombs", )}, /, {(, {"Meters", ^, 2}, )}}}, QuantityTF]](Files/ElectricSymmetryValue.en/9.png "TemplateBox[{InterpretationBox[, 1], {\"C\", , \"/\", , {\"m\", ^, 2}}, coulombs per meter squared, {{(, \"Coulombs\", )}, /, {(, {\"Meters\", ^, 2}, )}}}, QuantityTF]")
] and volume charge density 
in units of [![TemplateBox[{InterpretationBox[, 1], {"C", , "/", , {"m", ^, 3}}, coulombs per meter cubed, {{(, "Coulombs", )}, /, {(, {"Meters", ^, 3}, )}}}, QuantityTF]](Files/ElectricSymmetryValue.en/11.png "TemplateBox[{InterpretationBox[, 1], {\"C\", , \"/\", , {\"m\", ^, 3}}, coulombs per meter cubed, {{(, \"Coulombs\", )}, /, {(, {\"Meters\", ^, 3}, )}}}, QuantityTF]")
] is given by: - ElectricSymmetryValue with boundary unit normal
models: - Model parameters pars as specified for ElectrostaticPDEComponent.
- ElectricSymmetryValue is effectively the same as ElectricFluxDensityValue with an electric flux of 0.
- The boundary predicate pred can be specified as in NeumannValue.
- If the ElectricSymmetryValue depends on parameters
that are specified in the association pars as …,keypi…,pivi,…], the parameters 
are replaced with 
.
Examples
open allclose allApplications (1)
Model the right half of a dielectric region of a capacitor. Set up the electrostatic model variables 
:
Set up the right half-region 
:
Specify electrostatic model parameter relative permittivity 
:
Set up an electric potential at the upper boundary:
Text
Wolfram Research (2023), ElectricSymmetryValue, Wolfram Language function, https://reference.wolfram.com/language/ref/ElectricSymmetryValue.html.
CMS
Wolfram Language. 2023. "ElectricSymmetryValue." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ElectricSymmetryValue.html.
APA
Wolfram Language. (2023). ElectricSymmetryValue. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ElectricSymmetryValue.html