12.1.Magnetic Energy of Coupled Circuit
Thus, the magnetic energy of n coupled circuits is
U = (rigid circuits, linear media)
12.2.Energy Density in The Magnetic Field
U =
For the case of isotropic, linear, magnetic materials, the equation reduce to
12.3.Forces and Torques on Rigid Circuits
Suppose we allow one of the parts of the system to make a displacement dr under the influence of the magnetic force acting upon it, all currents remaining constant. The mechanical work performed by the force F acting on the system is
dW = F dr
12.4.Hysteresis Loss
let us treat the ferromagnetic specimen as forming part of a magnetic circuit. Then NI may be replaced by around a typical flux path,
where A is the cross section of the magnetic circuit appropriate to the lenght interval dI. Since dI is always tangent to the flux path, the preceding equation may be written as
where V is the volume of the magnetic circuit-that is, the region of space in which the magnetic field is different from zero.






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