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.

### 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 ...

### 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.

### Iron Sphere in a 60 Hz Magnetic Field

An iron sphere is exposed to a spatially uniform, sinusoidally time-varying, background magnetic field. The frequency of the field is low enough such that the skin depth is larger than the radius of the sphere. A reduced field formulation is used to impose the background field. Two approaches for solving this problem are shown. The induced currents in the sphere and the perturbation to the ...

### 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 ...

### 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 ...

### 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 ...

### Electromagnetic Force Calculation Using Virtual Work and Maxwell Stress Tensor

The model compare the electromagnetic force calculated by *virtual work* and *maxwell stress tensor* methods on the axial magntic bearing. The forces is evaluated by studying the effect of a small displacement on the electromagnetic energy of the system. This is done by using the *Magnetic Fields*, *Deformed Geometry* and *Sensitivity* physics interfaces.

### Modeling a Capacitive Position Sensor Using BEM

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_ ...

### 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.

### Operational Amplifier with Capacitive Load

An operational amplifier (op-amp) is a differential voltage amplifier with a wide range of applications in analog electronics. This tutorial models an op-amp connected to a feedback loop and a capacitive load. The op-amp is modeled as an equivalent linear subcircuit in the *Electrical Circuit* interface, where it is inserted into an outer circuit. The model is partially based on the SPICE ...