Magnetic Fields (mf)

Magnetostatics with out-of-plane currents (2D, 2D axisymmetric). Elmer MagnetoDynamics2D.

Category

AC/DC › Electromagnetic Fields

Name (tag)

mf

Space dimensions

2D, 2D axisymmetric

Studies

Stationary, Time Dependent

Dependent variables

Az Magnetic vector potential, z component (Wb/m)

Default features

Ampere’s Law, Initial Values, Magnetic Insulation

\(\nabla\times(\mu_0^{-1}\mu_r^{-1}\nabla\times\mathbf{A}) = \mathbf{J}_e\)

Material properties used: Relative permeability (μᵣ), Electrical conductivity (σ).

Interface settings

Setting Symbol Unit Default Choices / type

Discretization

Element order

Quadratic

Linear, Quadratic

Elmer Solver

Additional Elmer solver keywords
Lines appended verbatim to this interface’s Solver section in the .sif file

Text (multi-line)

Domain features

Ampere’s Law

Selection: Domains (all by default) · Physics ribbon › Domains, or right-click the interface in the Model Builder

\(\nabla\times\mathbf{H} = \mathbf{J},\quad \mathbf{B}=\nabla\times\mathbf{A},\quad \mathbf{B}=\mu_0\mu_r\mathbf{H}\)

Setting Symbol Unit Default Choices / type

Constitutive Relations

Relative permeability

μᵣ

From material

From material, User defined

mur

μᵣ

1

0

Expression

Electrical conductivity

σ

From material

From material, User defined

sigma

σ

S/m

0

Expression

External Current Density

Selection: Domains · Physics ribbon › Domains, or right-click the interface in the Model Builder

\(\mathbf{J} = \mathbf{J}_e\)

Setting Symbol Unit Default Choices / type

External Current Density

External current density, out-of-plane component

J_e,z

A/m^2

1e6

Expression

Initial Values

Selection: Domains (all by default) · Physics ribbon › Domains, or right-click the interface in the Model Builder

No settings.

Boundary features

Magnetic Insulation

Selection: Boundaries (all by default) · Physics ribbon › Boundaries, or right-click the interface in the Model Builder

\(\mathbf{n}\times\mathbf{A} = \mathbf{0}\)

No settings.

Magnetic Potential

Selection: Boundaries · Physics ribbon › Boundaries, or right-click the interface in the Model Builder

\(A_z = A_{0}\)

Setting Symbol Unit Default Choices / type

Magnetic Potential

Magnetic vector potential, z component

Wb/m

0

Expression

Perfect Magnetic Conductor

Selection: Boundaries · Physics ribbon › Boundaries, or right-click the interface in the Model Builder

\(\mathbf{n}\times\mathbf{H} = \mathbf{0}\)

No settings.

Result variables

Name Description Unit

Az

Magnetic vector potential, z component

Wb/m

mf.B

Magnetic flux density

T

mf.normB

Magnetic flux density norm

T

mf.normH

Magnetic field norm

A/m