Superposition principle with Ampère’s law and a semi-infinite wire

Abstract

In this article, a semi-infinite wire serves as a pedagogical example to demonstrate Ampère's law. To effectively apply the law, two conditions must be met: (i) the wire must form a closed circuit, and (ii) the current must have symmetry. Fulfilling requirement (i) involves connecting an additional semi-infinite wire at an arbitrary angle, ensuring that their far ends join at infinity to form a closed circuit. Although this additional wire disrupts current symmetry, condition (ii) can be satisfied by superposing multiple diagrams wherein the additional wires are arranged with symmetry. Ampère's law can then be utilized to determine the magnetic field generated by the wire arrangement. The analysis in this article is well-suited for introductory electromagnetism courses, highlighting the principle of superposition in physics.