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.

### 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 ...

### 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 ...

### Computing Intercepted Flux

This example model demonstrates four different approaches for computing the integrals of fields over arbitrarily placed geometries that can be re-positioned without having to re-solve the model. This approach is also useful if you want to integrate the results of a model over different sub-regions that you do not want to include in your original computational model. The example of computing ...

### 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.

### External Material, AC/DC Module, General HB/BH relation

The AC/DC magnetic interfaces now support material models defined in external C code. A new way to specify user-defined material models is included in COMSOL Multiphysics version 5.2. You can now access external material functions, written in C code, which have been compiled into a shared library. By writing a wrapper function in C code, you can also use material functions written in another ...

### Modeling of Wires, Surfaces, and Solids with Boundary-Element-Based Electrostatics

These examples demonstrate using the *Electrostatics, Boundary Elements* interface, introduced in version 5.3 of the COMSOL Multiphysics® software. In the blog post associated with these files, "[How to Create Electrostatics Models with Wires, Surfaces, and Solids](/blogs/how-to-create-electrostatics-models-with-wires-surfaces-and-solids/)", we demonstrate the pros and cons of using the boundary ...

### 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 ...

### 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_ ...

### 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.