MagneticPotentialCondition

MagneticPotentialCondition[pred,vars,pars]

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

MagneticPotentialCondition[pred,vars,pars,lkey]

represents a magnetic potential surface boundary condition with local parameters specified in pars[lkey].

Details

  • MagneticPotentialCondition specifies a Dirichlet boundary condition for MagnetostaticPDEComponent and MagneticPDEComponent.
  • MagneticPotentialCondition is typically used to set a specific magnetic potential on the boundary.
  • MagneticPotentialCondition sets a scalar magnetic potential on the boundary with dependent variable and independent variables .
  • Stationary variables vars are vars={Vm[x1,…,xn],{x1,…,xn}}.
  • MagneticPotentialCondition sets a vector magnetic potential on the boundary with dependent variable and independent variables .
  • The vector-valued dependent variable is specified as a three-vector ={Ax1,Ax2,Ax3}.
  • Stationary variables vars are vars={[x1,…,xn],{x1,…,xn}}.
  • Frequency-dependent variables vars are vars={[x1,…,xn],ω,{,…,xn}}.
  • Time-dependent variables vars are vars={[t,x1,…,xn],t,{x1,…,xn}}.
  • The following additional model parameters pars can be given:
  • parameterdefaultsymbol
    "MagneticPotential"
  • 0
    		• , magnetic surface potential in [TemplateBox[{InterpretationBox[, 1], "A", amperes, "Amperes"}, QuantityTF]]
    "MagneticPotential"
  • {0,…}
    		• , magnetic surface potential in [TemplateBox[{InterpretationBox[, 1], {"A", , "/", , {"m", ^, 2}}, amperes per meter squared, {{(, "Amperes", )}, /, {(, {"Meters", ^, 2}, )}}}, QuantityTF]]
  • Model parameters pars are specified as for MagnetostaticPDEComponent or MagneticPDEComponent.
  • MagneticPotentialCondition evaluates to one or more DirichletCondition instances.
  • The boundary predicate pred can be specified as in DirichletCondition.
  • If the MagneticPotentialCondition depends on parameters that are specified in the association pars as …,keypi…,pivi,…], the parameters are replaced with .

Examples

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Basic Examples  (4)

Set up a default magnetic potential boundary condition:

Set up a default magnetic vector potential boundary condition:

Set up a magnetic potential boundary condition with surface potential :

Set up a default magnetic vector potential boundary condition:

Scope  (2)

Define model variables vars for a magnetostatic analysis with named boundary condition model parameters pars:

Construct one of the boundary conditions:

Define model variables vars for a magnetic analysis with named boundary condition model parameters pars:

Construct one of the boundary conditions:

Applications  (3)

To model a permanent magnet in 2D with a rectangular cross section, define the mesh to use:

Visualize the internal boundaries of the magnet region:

Define the magnetostatic operator:

Define the zero magnetic scalar potential condition at the exterior boundaries:

Solve the magnetostatic PDE model:

Visualize the magnetic scalar potential and the magnetic field:

To model a 3D cylinder permanent magnet, set up variables:

Define the magnet region of height [TemplateBox[{InterpretationBox[, 1], "m", meters, "Meters"}, QuantityTF]] and radius [TemplateBox[{InterpretationBox[, 1], "m", meters, "Meters"}, QuantityTF]]:

Define the magnetization vector:

Set up boundary conditions:

Set up the mesh with a sphere of air of [TemplateBox[{InterpretationBox[, 1], "m", meters, "Meters"}, QuantityTF]] that represents the surrounding volume:

Visualize the magnet cylinder that is inside the mesh:

Set up the magnetostatIc PDE component:

Solve the PDE:

Visualize the magnetic field:

Define the mesh to model a long copper wire of circular cross section:

Define the wire region:

Define the air region:

Define the parameters of the model:

Define the variables:

Define the uniform external current density in the direction:

Define the magnetic equation:

Define a zero magnetic potential condition at the exterior boundary:

Define the PDE:

Set up an angular frequency of 800 Hz:

Replace the angular frequency of the equation with the frequency and solve the PDE:

Compute the electric field:

Compute the conduction current:

Extract the external current:

Compute the total current:

Visualize the total current magnitude:

Wolfram Research (2025), MagneticPotentialCondition, Wolfram Language function, https://reference.wolfram.com/language/ref/MagneticPotentialCondition.html.

Text

Wolfram Research (2025), MagneticPotentialCondition, Wolfram Language function, https://reference.wolfram.com/language/ref/MagneticPotentialCondition.html.

CMS

Wolfram Language. 2025. "MagneticPotentialCondition." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MagneticPotentialCondition.html.

APA

Wolfram Language. (2025). MagneticPotentialCondition. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MagneticPotentialCondition.html

BibTeX

@misc{reference.wolfram_2024_magneticpotentialcondition, author="Wolfram Research", title="{MagneticPotentialCondition}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/MagneticPotentialCondition.html}", note=[Accessed: 15-January-2025 ]}

BibLaTeX

@online{reference.wolfram_2024_magneticpotentialcondition, organization={Wolfram Research}, title={MagneticPotentialCondition}, year={2025}, url={https://reference.wolfram.com/language/ref/MagneticPotentialCondition.html}, note=[Accessed: 15-January-2025 ]}