# ElectricPotentialCondition

ElectricPotentialCondition[pred,vars,pars]

represents an electric potential surface boundary condition for PDEs with predicate pred indicating where it applies, with model variables vars and global parameters pars.

ElectricPotentialCondition[pred,vars,pars,lkey]

represents an electric potential surface boundary condition with local parameters specified in pars[lkey].

# Examples

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## Basic Examples(3)

Set up an electric potential surface boundary condition:

Set up a default electric potential surface boundary condition:

Compute the electric potential distribution with model variables and parameters with an electric potential of [] at the left boundary and a ground potential at the right boundary.

Specify model variables and electrostatic parameters:

Set up and solve an electrostatic PDE:

Visualize the solution:

## Scope(3)

Define model variables vars for an electrostatic analysis with model parameters pars and multiple specific parameter boundary conditions:

### 1D(1)

Compute the electric potential distribution between two parallel plates separated by a distance [] and positioned normal to the axis. The left plate is maintained at a constant potential [], whereas the right plate is grounded, . The region between the plates is characterized by a relative permittivity and a uniform electron charge density []. The equation to use in the model is given by:

Set up the electrostatic model variables :

Set up a region :

Specify electrostatic model parameters:

Specify the electric potential conditions:

Set up the equation:

Solve the PDE:

Visualize the solution:

### 3D(1)

Model a dielectric material of a cylindrical capacitor with two electric potential conditions at the upper and lower boundaries, which represent the capacitor electrodes. The equation to use in the model is given by:

Set up the electrostatic model variables :

Set up a region :

Specify a relative permittivity :

Specify ground potential at the lower boundary:

Specify an electric potential of [] at the upper boundary:

Set up the equation:

Solve the PDE:

Visualize the solution:

Wolfram Research (2023), ElectricPotentialCondition, Wolfram Language function, https://reference.wolfram.com/language/ref/ElectricPotentialCondition.html.

#### Text

Wolfram Research (2023), ElectricPotentialCondition, Wolfram Language function, https://reference.wolfram.com/language/ref/ElectricPotentialCondition.html.

#### CMS

Wolfram Language. 2023. "ElectricPotentialCondition." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ElectricPotentialCondition.html.

#### APA

Wolfram Language. (2023). ElectricPotentialCondition. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ElectricPotentialCondition.html

#### BibTeX

@misc{reference.wolfram_2024_electricpotentialcondition, author="Wolfram Research", title="{ElectricPotentialCondition}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/ElectricPotentialCondition.html}", note=[Accessed: 30-May-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_electricpotentialcondition, organization={Wolfram Research}, title={ElectricPotentialCondition}, year={2023}, url={https://reference.wolfram.com/language/ref/ElectricPotentialCondition.html}, note=[Accessed: 30-May-2024 ]}