374 ELEMENTS OF ELECTRICAL ENGINEERING. 



-1=5 



P\ 



in which the angle 6 is expressed in radians, L is the length in centimeters of the 

 two iron faces parallel to the line of intersection C, Fig. 14, and log p 2 /pj represents 

 the Naperian logarithm. 



Proof of equation (sj). The lines offeree in the air gap are arcs of circles with 

 their centers at C. Let & be the magnetomotive force between the iron faces. Consider 

 the magnetic flux A4> which crosses from face to face in the region Ar. The length 

 of air path along which A* crosses from face to face is rd. Dividing & by this length 

 of path gives the magnetic field intensity in the region Ar, according to equation 

 (i). The sectional area of the region Ar is L X Ar so that 



Integrating this expression from r = p l to r=p v we have 



or, since <I> = #7<$ from equation (10), we have equation (13) at once. 



(d ) Magnetic reluctance of a long air gap between inclined faces. Several modi- 

 fications of equation (13) have been proposed for the approximate calculation of the 

 reluctance of along air gap between inclined faces. These modifications are, how- 

 ever, of no value. The best approximate calculations may be made as follows : 



If the adjacent edges of the inclined faces are near together, always assume two 

 equal flat rectangular faces which represent the actual faces as nearly as one can judge, 

 and use equation (13). 



If the adjacent edges of the inclined faces are not very near together, take the mean 

 sectional area of the two faces for the mean sectional area s of the gap space, estimate 

 the mean length / of the gap as the length of a smoothly curved line starting from the 

 middle of one face at right angles to the face, and leading to the middle of the other 

 face and at right angles to it, and use equation (12). 



Note that the angle 6 between the two faces I and I of Fig 15 is 1 80 or IT. The 

 same is true of the faces 2 and 2, and of the faces 3 and 3. 



18. Two typical examples of magnetic leakage calculations. 



(a) When magnetic leakage is due to an air gap only, and not 

 to an opposing magnetomotive force. Magnetic leakage around a 

 dynamo armature when the armature current is zero. In most 

 dynamo calculations the actual useful flux <I> through the armature 



