WOLFRAM

Wolfram Language & System Documentation Center

MagneticFieldIntensity[vars,pars,spotential]

yields the magnetic field intensity from the scalar magnetic potential spotential .

MagneticFieldIntensity[vars,pars,vpotential]

yields the magnetic field intensity from vector magnetic potential vpotential .

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Applications  
See Also
Tech Notes
Related Guides
History
Cite this Page

MagneticFieldIntensity

MagneticFieldIntensity[vars,pars,spotential]

yields the magnetic field intensity from the scalar magnetic potential spotential .

MagneticFieldIntensity[vars,pars,vpotential]

yields the magnetic field intensity from vector magnetic potential vpotential .

Details

Examples

open all close all

Basic Examples  (2)

Compute the magnetic field intensity for a scalar :

Wolfram Language code: MagneticFieldIntensity[{Vm[x, y], {x, y}}, <||>, Subscript[V, m][x, y]]

Compute the magnetic field intensity for a vector potential :

Wolfram Language code: MagneticFieldIntensity[{{Ax[x, y, z], Ay[x, y, z], Az[x, y, z]}, {x, y, z}}, <|"VacuumPermeability" -> Subscript[μ, 0]|>, {Ax[x, y, z], Ay[x, y, z], Az[x, y, z]}]

Scope  (3)

Compute the magnetic field intensity for a vector potential with magnetization vector component :

Wolfram Language code: MagneticFieldIntensity[{{Ax[x, y, z], Ay[x, y, z], Az[x, y, z]}, {x, y, z}}, <|"VacuumPermeability" -> Subscript[μ, 0], "Magnetization" -> {0, Subscript[M, z][x, y, z], 0}|>, {Ax[x, y, z], Ay[x, y, z], Az[x, y, z]}]

Compute a reduced magnetic field intensity for a vector potential :

Wolfram Language code: MagneticFieldIntensity[{{0, 0, Az[x, y]}, {x, y}}, <|"VacuumPermeability" -> Subscript[μ, 0]|>, {Ax[x, y, z], Ay[x, y, z], Az[x, y, z]}]

Compute the magnetic field intensity for a scalar with magnetization vector component :

Wolfram Language code: MagneticFieldIntensity[{Vm[x, y], {x, y}}, <|"VacuumPermeability" -> Subscript[μ, 0], "Magnetization" -> {Subscript[M, x][x, y], 0}|>, Subscript[V, m][x, y]]

Applications  (2)

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

Wolfram Language code: mesh = \!\(\*GraphicsBox[«2»]\);

Visualize the internal boundaries of the magnet region:

Wolfram Language code: Show[HighlightMesh[mesh, {...}], PlotRange -> {{-0.08, 0.08}, {-0.15, 0.15}}]

Set up the variables and parameters:

Wolfram Language code: vars = {Vm[x, y], {x, y}}; pars = <|"Magnetization" -> {0, Piecewise[{{400000, RegionMember[Rectangle[{-0.05, -0.1}, {0.05, 0.1}]][{x, y}]}}, 0]}|>;

Solve the magnetostatic PDE model with a magnet transversely magnetized in the direction of the axis:

Wolfram Language code: VmFun = NDSolveValue[{MagnetostaticPDEComponent[vars, pars] == 0, MagneticPotentialCondition[x == -1 || x == 1 || y == -1 || y == 1, vars, pars]}, Vm[x, y], {x, y}∈mesh]

Compute the magnetic field intensity:

Wolfram Language code: fieldIntensity = MagneticFieldIntensity[vars, pars, VmFun]

Visualize the magnetic field intensity:

Wolfram Language code: Show[Graphics[{Gray, Rectangle[{-0.05, -0.1}, {0.05, 0.1}]}], StreamPlot[fieldIntensity, {x, -0.3, 0.3}, {y, -0.3, 0.3}, StreamColorFunction -> "Rainbow"]]

To model a long wire of circular cross section, define the mesh to use:

Wolfram Language code: mesh = [image];

Define a wire region:

Wolfram Language code: wireRegion = Disk[{0, 0}, 0.2];

Set up the variables and parameters:

Wolfram Language code: vars = {{0, 0, Az[x, y]}, {x, y}}; pars = <|"ExternalCurrentSource" -> {0, 0, Piecewise[{{1, RegionMember[wireRegion][{x, y}]}}, 0]}|>;

Solve the magnetic PDE model with a uniform current density in the direction in the wire:

Wolfram Language code: AFun = NDSolveValue[{MagneticPDEComponent[vars, pars] == 0, MagneticPotentialCondition[x ^ 2 + y ^ 2 >= 1, vars, pars]}, vars[[1]], {x, y}∈mesh]

Compute the magnetic field intensity:

Wolfram Language code: fieldIntensity = MagneticFieldIntensity[vars, pars, AFun]

Visualize the magnetic field intensity:

Wolfram Language code: Show[StreamPlot[fieldIntensity, {x, y}∈mesh], Graphics[{Darker[Orange], wireRegion}]]
Wolfram Research (2026), MagneticFieldIntensity, Wolfram Language function, https://reference.wolfram.com/language/ref/MagneticFieldIntensity.html.

Text

Wolfram Research (2026), MagneticFieldIntensity, Wolfram Language function, https://reference.wolfram.com/language/ref/MagneticFieldIntensity.html.

CMS

Wolfram Language. 2026. "MagneticFieldIntensity." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MagneticFieldIntensity.html.

APA

Wolfram Language. (2026). MagneticFieldIntensity. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MagneticFieldIntensity.html

BibTeX

@misc{reference.wolfram_2026_magneticfieldintensity, author="Wolfram Research", title="{MagneticFieldIntensity}", year="2026", howpublished="\url{https://reference.wolfram.com/language/ref/MagneticFieldIntensity.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_magneticfieldintensity, organization={Wolfram Research}, title={MagneticFieldIntensity}, year={2026}, url={https://reference.wolfram.com/language/ref/MagneticFieldIntensity.html}, note=[Accessed: 12-June-2026]}