COUPLE OF ROTATION OF TWO CIRCULAR CURRENTS. 165 



neglected, we get, making use of the value X given by equation (32), 



e=- 



(73) 



ss Ti , 'ftV'VA.sW.i 



r* ^2\ 2 J r^ 3 \2. 4 J r* 4 



-i 



*V 2 I 



J 



The value of the principal term is half that which corresponds to the 

 case in which the axis of the current passes through the centre of the 

 current S', which we already know. 



795. If the current S' be replaced by a magnet of length 2/, 

 making an angle 8 with the plane of the current, we find by reasoning 

 analogous to that of (746) that the couple produced by the action of 

 the current S on the magnet, provided we neglect expressions of a 



/ 2 

 higher order than , is expressed by 



= - 2/ COS 3 



When the current S is replaced by a coil of n windings with a 

 rectangular channel whose dimensions are 2b and 2<r, we have in 

 the same way, by integrating the value of X given by equation (31), 



in which a value very near - is assigned to 6, and neglecting terms 

 of a higher order than the square of the dimensions of the channel, 



P I 



-1 - ) + - 



2 \2/ r 2 3 \2.4/ r- 



i ^ / ^ \ 2 <r 2 ^ ^ 2 



(74) +--2 + (- ) ~2---2 



3 a 2 \2/ r 2 2 r 2 



