ELECTROMAGNETS. MAGNETISM OF IRON. 93 



58. Magnetic circuit calculations. When an iron rod of uni- 

 form size and quality forms a closed magnetic circuit and is 

 subjected to a uniform magnetizing force <$' along its entire 

 length, the value of the flux density cB in the rod may be found 

 from the cB and 3C curve, and the total flux through the rod 

 may be found by multiplying this flux density by the sectional 

 area of the rod. Or, the uniform value of 3f required to give 

 a specified total flux through the rod may be taken from the <$ 

 and cV curve, after the value of cB has been found, by dividing 

 the specified flux by the sectional area of the rod. 



When, however, the iron rod varies in size from point to point, 

 or when different parts of the rod are of different kinds of iron, or 

 when there is an air gap in the magnetic circuit, then some kind 

 of an averaging process must be used to calculate the magneto- 

 motive force required to produce a specified flux through the 

 rod, or, conversely, to calculate the flux produced by a specified 

 magnetomotive force. 



This calculation is carried out as follows: 



(a) To find the magnetomotive force required to produce a 

 specified flux. Divide the prescribed flux by the sectional area 

 in square centimeters of each part of the circuit, wrought iron, 

 cast iron, or air, as the case may be. This gives the flux density 

 cB in each part of the magnetic circuit. * Knowing cB for each 

 part of the circuit, take from the cB and 3f tables or curves 

 for the different kinds of iron, the value of &C required to produce 

 the known value of cB in each part of the circuit, and multiply 

 the value of 3f for each part of the circuit by the length in centi- 

 meters of that part. This gives the magnetomotive force re- 

 quired for each part; and the sum of these magnetomotive forces 

 is the total magnetomotive force required. This total magneto- 

 motive force may then be reduced to ampere-turns by multiplying 

 it by IO/47T. 



* It is here assumed that the whole of the magnetic flux passes through each 

 portion of the iron circuit. This is not always the case, for a portion of the mag- 

 netic flux may stray through the air. This portion is called the leakage flux. 

 Magnetic leakage is discussed in treatises on dynamo design. 



