THE MAGNETIC CIRCUITELECTROMAGNETS 21 



The total ampere-turns required in the exciting coil to produce 

 a flux of 1,000,000 lines across the air gap in path (1) are there- 

 fore 3,560 + 400 = 3,960, which is the answer to the problem. 



In all cases when there is no iron in the magnetic path, i.e., 

 when fj, = 1, as in the air gaps of dynamo-electric machines, the 

 required ampere-turns depend merely on the density B, and the 

 length I of the air gap. The fundamental relation, m.m.f, = HI 

 can then be written 0.4?r*S/ = Bl whence, 



SI per centimeter (in air) = 



L. 



similarly 



D 



SI per inch (in air) = 



2 54 



B = 2.02 B 



= 2B approximately 



(5) 



If the density is expressed in lines per square inch, 



B" 

 SI per inch (in air) = 5-= 



o.Z 



These formulas are easily remembered and are useful for making 

 rapid calculations. 



With a view to the more thorough understanding of electro- 

 magnetic problems likely to arise in the design of electrical 

 machinery, it should be observed that path (2) of the magnetic 

 system shown in Fig. 5 may be thought of as a shunt or leakage 

 path, the useful. flux being the 1,000,000 maxwells in the air 

 gap of path (1). It is important to note that this surplus or 

 leakage magnetism has cost nothing to produce, except in so 

 far as the total flux < 3 is increased in the common limb (3), 

 calling for a slight increase in the necessary exciting ampere- 

 turns. Even this small extra PR loss could be avoided by in- 

 creasing the cross-section A 3 of the common limb; but this would 

 generally add to the cost, not only because of the greater weight 

 of iron, but also because the length per turn of the exciting coil 

 would usually be greater, thus increasing the weight and cost of 

 copper if the PR losses are to remain unaltered. For these 

 reasons alone it is well to keep down the value of the leakage flux 

 in nearly all designs of electrical machinery; but the point here 

 made is that the existence of a magnetic flux, whether it be useful 

 or leakage magnetism, does not involve the idea of loss of energy 

 in the sense of an I 2 R loss which must always be associated with 

 the electric current. Attention is called to this matter in order 



