Main >>
Applications >>
Sample problems >>
Symmetric double line of conductors simulation

# HMagn2: Symmetric double line of conductors

This is an example of the symmetric double line of conductors simulation, performed with QuickField software.

**Problem Type:**

Plane problem of AC magnetics.

**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.

The complex impedance per unit length of the line can be obtained from the equation

*Z = ( V*_{1} - V_{2} ) / 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 of the double line *P* = 0.0000427 W/m.

Current density in symmetric double line of conductors:

Download simulation files