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Eddy currents inside plane conductor of linear permeable material can be excited in two ways: either by an external magnetic field, or by connecting the conductor to a load independent current source. If the excitation is time-harmonic and the frequency is low enough to neglect the displacement current, the modified vector potential describing the fields of the given plane eddy current problem is governed by a Helmholtz' equation. This equation can be solved by separation. The solution is inserted into the remaining boundary integral equation for the exterior vector potential in the domain surrounding the conductor yielding a system of linear equations. This method has been applied to a rectangular conductor. Numerical results will be given and compared with the results of commercial simulation software.