## Magnetostatics

The magnetostatic solution describes the distribution of static magnetic fields due to permanent magnets and continuous currents.

## Features

• 2D, 3D or axisymmetric Solution, static
• coupled with Thermal solution possible
• coupled with Elasticity solution possible
• Outputs Plot
• Magnetic Fluxdensity, Magnetic Fieldstrength
• Current Density
• Magnetic Potential (a-Pot)
• Nodal Force - virtual, Nodal Moment - virtual, ,Forcedensity - virtual, Lorentz Force
• Outputs Table
• Total Force - virtual, Total Moment - virtual, Total Lorentz Force
• RotorBand Torque - stresstensor, RotorBand Force - stresstensor
• Electrode Voltage, Current, Power
• Circuit Voltage, Current, Power
• Outputs 4D Fields
• Force - virtual, NodeID Table
• Forcedensity - virtual, XYZ Table

## Theory and Basics

### Formulations

The basis equations:
(1)        rot h = j
(2)        div b = 0
(3)        b = µ h

Boundary conditions:
(4)        n x h  | Γh = 0
(5)        n * b  | Γe = 0

Vectorpotential a:

(6)        b = rot a

Magnetostatic weak a-formulation:

(7)            ( µ-1 rot a, rot a’ )Ω
+ (-µ-1 bs, rot a’ ) Ω
+ (- ja’ ) ΩC
= 0, for all a’ element of Ω

### Basic Example: Team Problem 20: Static Force Analysis

Video

This example is a test case for electromagnetic analysis software tools. There are measured results available that we will use for comparison of our results.

Mesh of a quarter of the geometry.

## Results

Fluxdensity and Force

The magnetic Fluxdensity result is displayed as contourplot.

or following as vectorplot

The force is calculated on each node.

The measured reference result for 3000 A is 8.1 N. In Magnetics for NX / Simcenter, using a standards mesh, the result is 8.2 N.

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