HMagn2: Symmetric double line of conductors
This is an example of the symmetric double line of conductors simulation, performed with QuickField software.
Problem Type:
A plane problem of time-harmonic 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 = 1,000,000 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 = ( V1 - V2 ) / I
where V1 and V2 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 = 0.000493 + i 0.000732 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 = 0.0000437 W/m.
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