Magnetic flux density produced by finite-length twisted-wire pairs

Twisting a wire pair is often used to reduce the wire's low frequency magnetic flux density impinging upon spatially adjacent circuitry. Typically, predictions of the magnetic flux density due to the twisted-wire pair are based upon mathematical formulations for infinite-length wires. In the present work, expressions for predicting the quasistatic magnetic flux density near a finite-length, current-carrying twisted-wire pair are derived. These equations are numerically integrated, and the results compared with the magnetic flux density from the corresponding straight-wire pair, thereby yielding results useful for electromagnetic compatibility analyses. Additionally, approximate far-zone magnetic flux density equations are developed, and their range of validity established. These equations are useful for magnetic flux density estimations at distances further removed from the twisted-wire pair than the usual ones encountered in a typical enclosure. Also, they show that the large near-zone reduction of the magnetic flux density magnitude obtained by twisting the wire pair, relative to the straight-wire pair, is not available in the far-zone.