0195136047.pdf

12.1 BASIC PRINCIPLES OF ELECTROMECHANICAL ENERGY CONVERSION 509

Interaction

Current-carrying conductors, when placed in magnetic fields, experience mechanical force.
Considering only the effect of the magnetic field, theLorentz force equationgives the force
Fas

F=BlI (12.1.4)

when a current-carrying conductor of lengthlis located in a uniform magnetic field of flux
densityB, and the direction of the current in the conductor is perpendicular to the direction of the
magnetic field. The direction of the force is orthogonal (perpendicular) to the directions of both
the current-carrying conductor and the magnetic field. Equation (12.1.4) is often used in electric
machine analysis.
The principle of interaction is illustrated in Figure 12.1.4, in whichB ̄is the flux density,I ̄
the current, andF ̄the force. Shown in Figure 12.1.4(a) is the flux densityB ̄of an undisturbed
uniform field, on which an additional field is imposed due to the introduction of a current-carrying
conductor. For the case in which the current is directed into and perpendicular to the plane of
the paper, the resultant flux distribution is depicted in Figure 12.1.4(b). It can be seen that in the
neighborhood of the conductor the resultant flux density is greater thanBon one side and less
thanBon the other side. The direction of the mechanical force developed is such that it tends to
restore the field to its original undisturbed and uniform configuration. Figure 12.1.4(c) shows the
conditions corresponding to the current being in the opposite direction to that of Figure 12.1.4(b).
The force is always in such a direction that the energy stored in the magnetic field is minimized.
Figure 12.1.5 shows a one-turn coil in a magnetic field and illustrates how torque is produced by
forces caused by the interaction between current-carrying conductors and magnetic fields.

Alignment

Pieces of highly permeable material, such as iron, situated in ambient medium of low permeability,
such as air, in which a magnetic field is established, experience mechanical forces that tend to
align them with the field direction in such a way that the reluctance of the system is minimized (or
the inductance of the system is maximized). Figure 12.1.6 illustrates this principle of alignment

B

(a) (b) (c)

F

I

F

Figure 12.1.4Principle of interaction.

F

F

I

Figure 12.1.5Torque produced by forces caused by interaction of

current-carrying conductors and magnetic fields.