# HMagn1: Slot embedded conductor

Problem Type:
A plane problem of AC magnetic field.

Geometry:

A solid copper conductor embedded in the slot of an electric machine carries a current I at a frequency f.

Given:
Magnetic permeability of air μ = 1;
Magnetic permeability of copper μ = 1;
Conductivity of copper σ = 58,005,000 S/m;
Current in the conductor I = 1 A;
Frequency f = 45 Hz.

Problem:
Determine current distribution within the conductor and complex impedance of the conductor.

Solution:
We assume that the steel slot is infinitely permeable and may be replaced with a Neumann boundary condition. We also assume that the flux is contained within the slot, so we can put a Dirichlet boundary condition along the top of the slot. See HMagn1.pbm problem in the Examples folder for the complete model.

The complex impedance per unit length of the conductor can be obtained from the equation Z = V / I

where V is a voltage drop per unit length. This voltage drop on the conductor can be obtained in Local Values mode of the postprocessing window, clicking an arbitrary point within the conductor.

Comparison of Results:
 Re Z (Ohm/m) Im Z (Ohm/m) Reference: 0.00017555 0.00047113 QuickField 0.00017550 0.00047111

Reference:
A. Konrad, «Integrodifferential Finite Element Formulation of Two-Dimensional Steady-State Skin Effect Problems», IEEE Trans. Magnetics, Vol MAG-18, No. 1, January 1982.

See the HMagn1.pbm problem in the Examples folder.