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Magnetically Permeable Sphere in a Static Magnetic Field

A sphere of relative permeability greater than unity is exposed to a spatially uniform static background magnetic field. Two formulations are used to solve this problem, and the differences between these are discussed. The field strength inside the sphere is computed and compared against the analytic solution.

Small-Signal Analysis of an Inductor

If an inductor's magnetic material is nonlinear, then the inductance depends on the current passing through it. This model consists of an inductor with a nonlinear magnetic core, where the small-signal inductance is simulated as a function of current. The model also investigates how the small-signal inductance depends on the DC current.

Applying a Current-Voltage Switch to Models

This example exemplifies how to model the switching between current and voltage excitations in *Terminal* boundary conditions. A more detailed description of the phenomenon and the modeling process can be seen in the blog post "[Control Current and Voltage Sources with the AC/DC Module](https://www.comsol.com/blogs/control-current-and-voltage-sources-with-the-acdc-module/)".

Modeling a Capacitive Position Sensor Using FEM

This tutorial model explains how to extract lumped matrices by means of the *Stationary Source Sweep* study. The capacitance matrix of a five-terminal system is used to infer the position of a metallic object similar to real-world capacitive position sensors. The example illustrates the use of FEM, which is supported by the *Electrostatics* interface. When FEM is used, a volumetric mesh of a ...

Axisymmetric approximation of 3D Inductor

Inductive devices experience capacitative coupling between conductors at high frequencies. Modeling this phenomenon requires that you describe electric fields that have components both parallel with and perpendicular to the wire. This consideration might lead to the conclusion that a 3D model is always necessary to model the phenomenon, even if the coil is a helix, which is actually not the ...


Magnetotellurics is a method for estimating the resistivity profile of the Earth's subsurface using the natural electromagnetic source provided by the ionosphere. This model was defined by Zhdanov et al. in a study published in 1997. In this article, various scientific groups compared software performance on the same models. This is the model called COMMEMI-3D-2, which has become one of the ...

Iron Sphere in a 13.56 MHz Magnetic Field

An iron sphere is exposed to a spatially uniform, sinusoidally time-varying, background magnetic field. The frequency of the field is so high that the skin depth in the sphere is much smaller than the radius. At such high frequencies it is possible to model only the fields and induced currents on the surface of the sphere, thus avoiding the need for solving for the fields within the volume of ...

Contact Impedance Comparison

The contact impedance boundary condition is meant to approximate a thin layer of material that impedes the flow of current normal to the boundary, but does not introduce any additional conduction path tangential to the boundary. This example compares the contact impedance boundary condition to a full-fidelity model and discusses the range of applicability of this boundary condition.

Quadrupole Lens

Just like optical lenses focus light, electric and magnetic lenses can focus beams of charged particles. Systems of magnetic quadrupole lenses find a common use in focusing both ion and particle beams in accelerators at nuclear and particle physics centers. This model shows the path of ions going through three consecutive magnetic quadrupole lenses. The model also takes fringing fields ...

Electric Shielding Comparison

The electric shielding boundary condition is meant to approximate a thin layer of highly conductive material that provides an additional current path tangential to a boundary. This example compares the electric shielding boundary condition to a full-fidelity model and discusses the range of applicability of this boundary condition.