14 Prof. J. Larmor on Electromagnetic Induction 



therefore 



-1 + ip. 



Taking real parts only, we find that if 



P acA coss(/>, 

 then 



. — cos s<£ — p sin s<j> 



Jti OCAn ^ ; *> 



1 U 1 +p 2 



oc — A cosa .cos (s<£ — a), . . . (9) 

 where tana = p; and for the total inside field, we have 

 Po + Px QcA sinacos Iscj) + 5- — a J; 



which shows a lagging of ( ^ — a js, while the intensity is re- 

 duced in the ratio of sin a to unity. 



In a uniform field, whose magnetic force is F , the poten- 

 tial due to the rotating shell will be 



Fa 3 cos <f> +p sin <£ 



where 



_ 3R 

 * "" 47ra&> ' 



and the shell will therefore have the same outside effect as a 

 simple magnet of moment ¥a d /2vl+p 2 , whose axis is inclined 

 to the direction of the force at an angle tan" 1 p. 



The opposing couple experienced by the rotating shell will 

 therefore be the same as for this magnet, i. e, it will be 



G=F 2 a d p/2(l+p 2 ); 



and the rate of expenditure of power required to keep up the 

 rotation will be q^ 



[For a Delezenne's ring, of the same thickness and diameter, 

 and 1 centim. in breadth, rotating in the same field, we have 



~ . Tra 2 sin rf> -^ 



Current = -^ ^-coJb : 



lira . li 



rate of expenditure of power in driving it 



7ra 3 ft) 2 sin 2 (j> ™ 

 2R > 



