Energy considerations concerning current loops and magnetic objects

In the thermodynamics of compound magnetic systems there is an ambiguity in defining the free energies connected to the constituent parts or subsystems. It is argued that the choice, usually made in defining the energy of a magnetized body, leads to an expression for the energy of a current loop or coil of the form U?(L−italic)=i2+iϕa, where i and ϕa (an externally aplied flux, coupled to the loop) are considered as independent variables. With this expression a convention to decompose compound magnetic systems into subsystems can be given, which fits to the rules applied for nonmagnetic systems. Analogous to the case of a coil, an expression for the energy of a charged particle in a magnetic field can be derived which results in an expression for the Hamiltonian, which is generally applicable.