Calculation of magnetic dipole moment of torus knots

TL;DR

This paper presents a method to calculate the magnetic dipole moment of torus knots, extending classical concepts to complex three-dimensional loops and demonstrating their magnetic properties.

Contribution

It introduces a calculation approach for the magnetic moment of torus knots, a novel application beyond traditional planar loops.

Findings

Magnetic moment of torus knots can be computed using current and vectorial area.

The magnetic moment of complex 3D loops can be simplified as a product of current and loop area.

Torus knots serve as illustrative examples for magnetic moment calculations in non-planar loops.

Abstract

The magnetic moment of a closed loop with a steady current distribution is thoroughly described in many classical physics textbooks. Although usually the examples studied assume plane loops for explicit calculations of the magnetic moment, many other loop forms can be calculated. Among them, there are the torus knots. In this work, we explain how to calculate the magnetic moment of such current arrangement, and how it can be used as an interesting example that, even on three-dimensional loops, the magnetic moment can be taken as a simple product of the current and the vectorial area of the loop.