# Application Gallery

The Application Gallery features COMSOL Multiphysics® tutorial and demo app files pertinent to the electrical, structural, acoustics, fluid, heat, and chemical disciplines. You can use these examples as a starting point for your own simulation work by downloading the tutorial model or demo app file and its accompanying instructions.

Search for tutorials and apps relevant to your area of expertise via the Quick Search feature. To download the MPH-files, log in or create a COMSOL Access account that is associated with a valid COMSOL license. Note that many of the examples featured here can also be accessed via the Application Libraries that are built into the COMSOL Multiphysics® software and available from the File menu.

### 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.

### Capacitive position sensor

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 ...

### A Geoelectrical Forward Problem

The classical forward problem of geoelectrics (includes electrical resistivity tomography, ERT and earlier techniques as vertical electric sounding, VES) is the calculation of potentials at a given set of electrodes (M,N) while current is injected at other electrodes (A,B) into the ground. Typically the physical domain (earth) is unbounded to the sides and the bottom because of which one needs ...

### 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/)".

### Magnetotellurics

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 ...

### Capacitive position sensor, boundary elements

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 rather like real-world capacitive position sensors. The example illustrates the use of the boundary element method (BEM), which is supported by the _Electrostatics, Boundary Elements_ ...

### 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 ...

### Capacitance Matrix of Two Spheres

This model compares the numerical and analytical solutions for the capacitance matrix of two nonconcentric spheres. It also illustrates the relation between the Maxwell capacitance matrix and the mutual capacitance matrix.