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

$$-\nabla \text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\left(\frac{1}{\mu}\nabla {E}_{c}\right)+\left(j\omega \sigma -{\omega}^{2}\epsilon \right){E}_{c}=0$$

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 *ε _{c}* is

The boundary conditions associated with AC power electromagnetics
are a Dirichlet boundary condition, specifying the value of the electric
field *E _{c}* on the boundary,
and a Neumann condition, specifying the normal derivative of

For details, see AC Power Electromagnetics.

PDE | Solve partial differential equations in 2-D regions |

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.

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

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

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

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