Calculation of magnetic dipole moment of torus knots

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.