Surface Currents in a Circular Wire
Skin effect is a phenomenon where an alternating current tends to flow and distribute itself along the surface layer or outside skin of a conductor. This effect can for example be taken advantage of in power transmission applications by layering inexpensive conductor materials (for example aluminium) with a thin layer …
Microstrip Transmission Line
A shielded electrical microstrip transmission line is fixed to a substrate and placed in a shielded container of air. The simulation applies a known voltage to the strip to calculate the resulting capacitance and compares this with the theoretical result. The problem assumes symmetry in the lengthwise direction so that …
Stress Distribution in a Solenoid
This multiphysics model examines how magnetic forces give rise to stresses in a long thick cylindrical solenoid. A current density of 106 A/m2 is running through a wound coil with 1 cm inner to 2 cm outer radii. The material of the coil is assumed to have a modulus of elasticity of 1.075⋅1011 N/m2 and Poisson’s …
Inductance in Parallel Wires
This example calculates the inductance between parallel wires. Two 1 m wires with 4 mm radius 1 A current are placed 0.5 m apart in a large domain of non-conducting air or vacuum. The inductance is computed with both using the magnetic field energy and flux linkage, and compared against the analytical solution L = …
Conducting Sphere
This verification example considers a perfectly conducting sphere placed between two charged capacitor plates. An axisymmetric solution for the electrostatic potential is compared with a full 3D one, and verified against the analytical solution U(xi) = E0*(r3/xi2 - xi), where the electrical field is the potential …
Piezo Electric Bending of a Beam
Multiphysics simulation of piezoelectric bending of a laminated beam as for example can be found in actuators for MEMS (micro electro mechanical systems) devices. The model features coupled plane-stress and electrostatics physics modes with equations modified to account for the anisotropic piezo-electric coupling. The …
Magnetic Field Around a Permanent Magnet
Example of simulation and visualization of the two-dimensional static magnetic potential field around a u-shaped permanent magnet. This model is available as an automated tutorial by selecting Model Examples and Tutorials… > from the File menu. Or alternatively, follow the linked step-by-step instructions. …
Resistive Heating in a Tungsten Filament
This example models resistive Joule heating where the resulting current from an applied electric potential will heat a thin spiral shaped Tungsten wire, such as can be found in incandescent light bulbs. The filament reaches an equilibrium temperature where the internal heat generation is balanced by radiative heat loss …
Spherical Capacitor
Model of an electrostatic spherical capacitor. The example makes use of a 2D axisymmetric approximation with three subdomains, where an electric charge is applied between the middle insulating layer. For this configuration the analytic capacitance can be calculated as 4*πεrε0/dr, where dr is the thickness of the …
Two Material Wave Guide Interface
This example studies the interface between two different materials in a section of a wave guide. The change in material causes the waves to travel at different speeds. This changing diffraction pattern of the planar time harmonic waves can be investigated by using the Helmholtz equation for the amplitude of the waves A …