Magnetostatic Analysis

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Magnetostatics is the study of static magnetic fields.In electrostatics, the charges are stationary, whereas here, the currents are steady or dc(direct current). As it turns out magnetostatics is a good approximation even when the currents are not static as long as the currents do not alternate rapidly.Furthermore, Maxwell's displacement current that couples the electric and magnetic fields is assumed to be null.


In Magnetostatic analysis, the Gauss's law for magnetism, i.e. divergence of magnetic flux density is null, and Ampère's law, i.e. the curl of the magnetic field is equal to the static electric current density, are invoked to compute the magnetic field and its related quantities due to electric currents and permanent magnets.It has many practical applications, including:

  • Motors and generators
  • Linear and rotational actuators
  • Relays
  • MEMS
  • Magnetic recording heads
  • Magnetic levitation
  • Solenoids
  • Loud speakers
  • Electromagnetic Brakes and Clutches
  • Magnetic bearings
  • MRI
  • Sensors


The Magnetostatic module outputs the following results for each study:

  • Magnetic field
  • Magnetic flux density
  • Current density
  • Force density
  • Inductance matrix
  • Flux linkage
  • Resistance
  • Force
  • Torque
  • Stored energy
  • Temperature
  • Temperature gradient
  • Heat flux

Examples of design issues

The Magnetostatic module can help study a large number of devices and address numerous magnetic and electromechanical phenomena.Below is just a partial list:

  • Avoid saturation in magnetic devices. Magnetic saturation is a limitation occurring in ferromagnetic cores. Initially, as current is increased the flux increases in proportion to it.At some point, however, further increases in current lead to progressively smaller increases in flux.Eventually, the core can make no further contribution to flux growth and any increase thereafter is limited to that provided by air - perhaps three orders of magnitude smaller.
  • Minimize the cogging torque.The cogging torque of electrical motors is the torque due to the interaction between the permanent magnets and the stator slots of a Permanent Magnet (PM) machine. Also termed as detent or 'no-current' torque, it is an undesirable component for the operation of such a motor. It is especially prominent at lower speeds, with the symptom of jerkiness.
  • Lower cost and weight of magnetic devices by trimming excess material from ferromagnetic cores.
  • Optimize magnetic and ferromagnetic circuits.
  • Optimize coil winding and electromagnets.
  • Optimize permanent magnet machines by studying the trade-off between samarium-cobalt, Neodymium-iron-born, ceramic, and Alnico magnets.
  • Study the trade-off between soft magnetic and hard magnetic materials in terms of magnetization and demagnetization.
  • Study the effect of B-H curves or magnetization curves on the performance of magnetic devices and circuits.
  • Optimize the torque in motors while maintaining the driving current to a minimum.
  • Avoid sparking and thus minimizing brush wear and electric noise in motors, solenoids, actuators, and other electromechanical devices.
  • Optimize the force for linear solenoids and the torque for rotary solenoids without overheating the winding.
  • Assure the proper Lorentz force in a speaker voice coil.
  • Evaluate complex coil structures.
  • Evaluate a multitude of permanent magnet configurations.