Limitations of the Two-Step Darwin Model in Frequency Domain

In many technical applications at low frequency, wave propagation effects can be neglected, and Darwin models promise to accurately describe the electromagnetic fields because they include resistive, inductive, and capacitive terms. In a former work, we developed an efficient, frequency stable method to solve the full Maxwell model, i.e., without neglecting any effect. This method employs the electro-quasistatic gauge, which allows to cleanly separate the calculation of capacitive effects in a first step, from the calculation of inductive effects in a consecutive second step. The Darwin model in frequency domain and electro-quasistatic gauge can easily be derived from this method by neglecting just one term, namely the induced displacement current. Here, we compare this Darwin model with the full Maxwell model, e.g., for the example of an RLC -series circuit. We found that this Darwin model cannot describe the interaction between L and C in the RLC -circuit.