This paper proposes a 2D semi-analytical electromagnetic model to compute the magnetic field and eddy current generated by a variable current density along a conducting billet of induction heater. The developed model is based on the combination of the discretization method and the Biot-Savart theory. Firstly, the analytical solutions of the vector potential and the magnetic field are calculated in all elements discretized cylindrical geometry using the law of Biot-Savart. Then, the total field is determined by the contribution of the superposition of each element of the discretized geometry. The eddy currents are computed using the Ampere law, and it also allows us to determine the exact resulting heating power density, which is the heat source of the thermal problem. The results obtained are in agreement with those obtained using finite element method. Therefore, the developed magnetic model presents a fast and accurate tool for the design of induction heating devices.
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