1 10 ELEMENTS OF ELECTRICITY AND MAGNETISM. 



The simplest absolute electrodynamometer is that devised by Wilhelm Weber in 

 1846. It consists of a large stationary coil mounted with its plane vertical, and a 

 small circular coil suspended at its center by two fine wires. The current / to be 

 measured flows through both coils. The magnetic field produced by the outer coil at 



Fig. 75. 



its center is ff= 2irZ' ' Jjr' ', where Z / is the number of turns of wire in the large 

 coil and r' is its radius. This magnetic field exerts a torque 7"= Trr" Z" 'Iff cos, 6 

 upon the -small coil, where Z" is the number of turns of wire in the small coil, r" is 

 its radius and 8 is the angle between H and the plane of the small coil or, in other 

 words, 6 is the complement of the angle between the planes of the two coils. Sub- 

 stituting the value of ff=2TrZ / 7/r / in the expression for T, we have 



_ 

 T= 



cos 



This equation permits the calculation of / when Z', Z", r', and r" are known, 

 and when T and 6 have been observed. When c.g.s. units are used in equation 

 (41), the current is given in abamperes. 



Figure 75 shows a slightly modified form of Weber's absolute electrodynamometer 

 in which the small coil is suspended in the approximately uniform field between two 

 large circular coils side by side. 



The Siemens electrodynamometer. The force action between 

 two coils is proportional strictly to the square of the current 

 which flows through the two coils whatever the shape and rela- 

 tive position of the two coils may be, provided only that the 

 relative position of the two coils does not change. Therefore, if 



