A microscopic theory for the calculation of magnetic field induction of nanowires

The narrower a conductor the more significant is its induced magnetic field, or the Ørsted magnetic field. The calculation of the Ørsted magnetic field in current-carrying wires is a standard textbook exercise that generally assumes that the wire has a circular cross-section, and where a simplified form of the Biot–Savart equation is applied. While such formalism can be suitable for macroscopic wire structures, it will not be ideal for nano-sized wire structures because of the presence of structural features that might impact detailed structure of the Ørsted magnetic field. This work introduces a microscopic approach for the prediction of the Ørsted magnetic field in nanowires. The approach combines the current magnetization hypothesis (Tawfik, 2022) with molecular dynamics that applies the electron force field. The formalism can be utilized for predicting the Ørsted magnetic field of more complex nano-conductors. • The work introduces a microscopic approach to predict the Ørsted magnetic field. • Combines the current magnetization hypothesis with MD within the electron force field. • The theory is demonstrated for a lithium nanowire.