Design of Rotating Electrical Machines, 2nd Edition

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Principal Laws and Methods in Electrical Machine Design

1.1 Electromagnetic Principles

A comprehensive command of electromagnetic phenomena relies fundamentally on Maxwell’s equations. The description of electromagnetic phenomena is relatively easy when compared with various other fields of physical sciences and technology, since all the field equations can be written as a single group of equations. The basic quantities involved in the phenomena are the following five vector quantities and one scalar quantity:

Electric field strength	E	[V/m]
Magnetic field strength	H	[A/m]
Electric flux density	D	[C/m2]
Magnetic flux density	B	[Vs/m2], [T]
Current density	J	[A/m2]
Electric charge density, dQ/dV	ρ	[C/m3]

The presence of an electric and magnetic field can be analyzed from the force exerted by the field on a charged object or a current-carrying conductor. This force can be calculated by the Lorentz force (Figure 1.1), a force experienced by an infinitesimal charge dQ moving at a speed v. The force is given by the vector equation

(1.1)

Figure 1.1 Lorentz force dF acting on a differential length dl of a conductor carrying an electric current i in the magnetic field B. The angle β is measured between the conductor and the flux density vector B. The vector product i dl × B may now be written in the form i dl × B = idlB sin β.

In principle, this vector equation ...