ELECTROMAGNETS. MAGNETISM OF IRON. 8l 



coil of wire as shown in Fig. 59. Let & be the magnetomo- 

 tive force along the dotted path, and let m be the strength of 

 the pole N which has been carried around the path. Then, 

 according to Art. 47, &m is the work done on the pole by the 

 magnetic field of the coil. This work done on the moving pole 

 by the magnetic field of the coil is the work which is spent in keep- 

 ing the current constant in spite of the electromotive force induced 

 in the coil by the moving pole. This is evident when we consider 

 that work done on the pole by the field must be made good, that 

 is, -energy must be supplied from somewhere; and when we con- 

 sider that the energy stored in the system is the same in Figs. 58 

 and 59. Therefore, the only possible source of the energy for 

 doing work on the moving pole is the work that is done to keep 

 the current in the coil constant. 



Now the two poles of the flexible magnet are in the same 

 positions before and after the movement; therefore, of the total 

 number of lines of force which radiate from these poles, the same 

 number pass through the coil before and after the movement. 

 On the other hand, the flux ^irm (see Art. 26), which passes 

 along the magnet from pole to pole, passes through the coil after 

 the movement, so that the flux through the opening of the coil 

 is increased by the amount ^irm by the movement of the pole. 

 Therefore, according to equation (4), Zi X 4irm is the work 

 spent in keeping the current constant during the movement of 

 the pole and, since this is equal to the work cfm done upon the 

 pole by the magnetic field of the coil, we have 



&m = 4-jriZm 

 or 



& = 4irZi 



50. Units of magnetomotive force. The product IM (length 

 of path in centimeters multiplied by intensity of magnetic field 

 in gausses) gives the magnetomotive force along the path (when 

 / and <# are parallel, of course) in c.g.s. units. The name gilbert 

 has been adopted by the American Institute of Electrical Engi- 

 neers for the c.g.s. unit of magnetomotive force. 

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