CHAP. IVJ INDUCED E.M.F. 59 



Substituting in this equation the value of e from (25), and integ- 

 rating, we get 



(26) 



This shows that the average value of an induced e.m.f. does 

 not depend upon the law according to which the flux changes wit h 

 the time, and is simply proportional to the average rate of change 

 of the flux. 



As another special form of eq. (25) consider a straight con- 

 ductor of a length I centimeters moving at a velocity of v centi- 

 meters per second across a uniform magnetic field of a density of B 

 webers per sq. cm. Let B, /, and v be in three mutually perpendic- 

 ular directions. The flux d cut by the conductor during an infini- 

 tesimal element of time dt is equal to Blvdt. Substituting this 

 value into eq. (25) we get, apart from the sign minus, 



e=Blv (27) 



Should the three directions, B } I, and v, be not perpendicular to 

 each other, I in eq. (27) is understood to mean the projection of 

 the actual length of the conductor, perpendicular to the field, and 

 v is the component of the velocity normal to B and /. Both B and 

 v may vary with the position of the conductor, in which case eq. 

 (27) gives the value of the instantaneous voltage. If, at a cer- 

 tain moment, the various parts of the conductor cut across a field 

 of different density, eq. (27) must be written for an infinitesimal 

 length of the conductor, thus: de=Bv-dl, and integrated over 

 the whole length of the conductor. 



Besides the rule given above, the direction of the e.m.f. indin < ! 

 by the generator action can also be determined by the familiar 

 three-finger rule, due to Flemin i von in handlwoks and !<- 



mentary books on electricity. This rule is useful beause it empha- 

 sizes the three mutually perpendicular di: those of the 

 flux, the conductor, and the relative motion. In applying this 

 rule to a machine with a stationary armature one must remember 

 that the direction of the motion in Kleminiz's rule is that of the 

 conductor, and therefore is opposite to the direction of the actual 

 motion of the magnetic field. 



Problem 1. A secondary winding is j. laced on the rinr -id is 



.ted to a halli ! ' t tin- nun in the 



dary winding l>c n, the fln\ linking with each turn l>o wcUrs, and 



