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AC Power Electromagnetics

Solve PDEs that model harmonic electrical fields in conductors

The AC power electromagnetics problems are found when studying motors, transformers, and conductors carrying alternating currents. The Helmholtz's equation

·(1μEc)+(jωσω2ε)Ec=0

describes the propagation of plane electromagnetic waves in imperfect dielectrics and good conductors (σ » ωε). Here, ω is the angular frequency, ε is the coefficient of dielectricity, µ is the magnetic permeability, and σ is the conductivity. Complex permittivity εc is εc = ε-/ω. The conditions at material interfaces with abrupt changes of ε and µ are typical for the variational formulation and do not require special attention.

The boundary conditions associated with AC power electromagnetics are a Dirichlet boundary condition, specifying the value of the electric field Ec on the boundary, and a Neumann condition, specifying the normal derivative of Ec. This is equivalent to specifying the tangential component of the magnetic field Ht=jωn·(1μEc).

For details, see AC Power Electromagnetics.

Apps

PDE Solve partial differential equations in 2-D regions

Topics

Programmatic Workflow

Wave Equation

Solve the wave equation using the PDE app and the command line.

Helmholtz's Equation on a Unit Disk with a Square Hole

Solve a Helmholtz equation using the solvepde function.

PDE App Workflow

AC Power Electromagnetics

Analyze the skin effect produced by AC current carried by a wire with circular cross section.

Wave Equation

Solve the wave equation using the PDE app and the command line.

Scattering Problem

Solve a simple scattering problem computing the waves reflected from an object illuminated by incident waves.

Concepts

Hyperbolic Equations

Mathematical definition and discussion of the hyperbolic equation

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