Correct voltage distribution for axisymmetric sinusoidal modeling of induction heating with prescribed current, voltage, or power

We consider the problem of determining the voltage in coil rings, which arise as an axisymmetric approximation of a single connected induction coil during modeling of induction heating. Assuming axisymmetric electromagnetic fields with sinusoidal time dependence, we compute the voltages from the condition that the total current must be equal in each ring. Depending on whether total current, total voltage, or total power is prescribed, different linear systems of complex equations represent the ring voltages. In two sets of numerical simulations, varying the number of coil rings, we compare results using the correct voltage distribution to the corresponding results using the simple homogeneous voltage distribution.