THE MEASUREMENT OF CURRENT 75 



In elect rodynamometers when used with direct currents, H' 

 is the sum of the field due to the current circulating in the fixed 

 coils which form a part of the instrument, and the local field. 



An approximate expression for the turning moment acting 

 on the movable coil, assuming it to be a plane circuit, may be 

 obtained. 



Referring to Fig. 37, the field at the po'nt 0, the center of the 

 fixed coil, may be obtained as follows: Let the number of turns 

 per centimeter of length of the coil be n and let x be the axial dis- 

 tance of a turn from the center. If I P is the current in the wire, 

 a belt of winding bx cm. long will produce at the center a field 

 whose component along the axis is 



The effect of the whole coil will be 



T+> dx_ _ x_ l + 6 _ 4*nlrb 



If AV is the total number of turns 



H = 



If the movable coil of N M turns has a radius r, and the field in 

 which it is placed is uniform and of strength H, the mutual in- 

 ductance between the fixed and movable coils is 



2r*r*N M Nr cos 

 m = Hirr*N M cos = - 



W + 6 2 



where is the angle between the axes of the coils. 

 The turning moment is 



dm 2Tr*r 2 N M I AI N f Ir sin 



'-* -* F* Af f\ 



+ 

 and when the axes are perpendicular, this becomes 



M 



As implied above, the turning moment due to the mutual ac- 



