**Problem Type:**

A plane problem of AC magnetic field.

**Geometry:**

Two copper square cross-section conductors with equal but opposite currents are contained inside rectangular ferromagnetic coating. All dimensions are in millimeters.

**Given:**

Magnetic permeability of air *μ* = 1;

Magnetic permeability of copper *μ* = 1;

Conductivity of copper *σ* = 56,000,000 S/m;

Magnetic permeability of coating *μ* = 100;

Conductivity of coating *σ* = 10,000,000 S/m;

Current in the conductors *I* = 1 A;

Frequency *f* = 100 Hz.

**Problem:**

Determine current distribution within the conductors and the coating, complex impedance of the line, and power losses in the coating.

**Solution:**

We assume that the flux is contained within the coating, so we can put a Dirichlet boundary condition on the outer surface of the coating. See HMagn2.pbm problem in the Examples folder for the complete model.

The complex impedance per unit length of the line can be obtained from the equation *Z = ( V _{2} - V_{1} ) / I*

where *V*_{1} and *V*_{2} are voltage drops per unit length in each
conductor. These voltage drops are equal with opposite signs due to the symmetry of the model.
To obtain a voltage drop, switch to Local Values mode in postprocessing window, and then pick an
arbitrary point within a conductor.

The impedance of the line *Z* = 0.000484 + *i* 0.000736 Ohm/m.

To obtain power losses in the coating:

In the postprocessing mode, choose

**Pick Elements**and pick the coating block to create the contour.Choose

**Integral Values**and select*Joule heat*from the list of integral quantities and choose**Calculate**.

The power losses in the coating *P* = 0.0000427 W/m.

See the *HMagn2.pbm* problem in the Examples folder.