0195136047.pdf

508 ELECTROMECHANICS

Motional emfe=BlU (12.1.3)

which is often called thecutting-of-fluxequation, whereBis the flux density of a non-

time-varying, uniform magnetic field,lis the length of the conductor,Uis the velocity

of the conductor, andB ̄,l ̄, andU ̄are mutually perpendicular in their directions. If the

motion is rotary in nature, it is also known asrotational voltage. The direction for the

motional emf can be worked out from theright-hand rule:if the thumb, first, and second

fingers of the right hand are extended so that they are mutually perpendicular to each

other, and if the thumb represents the direction ofU ̄and the first finger the direction of

B ̄, the second finger will then represent the direction of the emf alongl ̄. This is depicted

in Figure 12.1.3(a).

The generation of motional emf is further illustrated by a simple example, as shown

in Figure 12.1.3(b), where a single-turn coil formed by the moving (or sliding) conductor

(moving with velocityU), the two conducting rails, and the voltmeter are situated in a

magnetic field of flux densityB. The conductor moving with a velocityU, in a direction at

right angles to bothBandl, sweeps the arealUin 1 second. The flux per unit time in this

area isBlU, which is also the flux linkage per unit time with the single-turn coil. Thus,

the induced emfeis simply given byBlU. The motional emf (or speed emf) is always

associated with the conversion of energy between the mechanical and electrical forms.

3. The coil may move through a time-varying flux; that is to say, both changes (1) and (2)
   may occur together. Usually one of the two phenomena is so predominant in a given device
   that the other may be neglected for the purposes of analysis.

Because magnetic poles occur in pairs (north and south) and the movement of a conductor

through a natural north–south sequence induces an emf that changes direction in accordance with

the magnetic polarity (i.e., an alternating emf), the devices are inherently ac machines.

U

U

Figure 12.1.3Generation of motional emf.(a)Right-hand rule.(b)Simple example.