47 PARTICULAR CASES. 



486. ELECTRODYNAMIC ROTATION. Consider an unlimited 

 rectilinear current X'X of strength I (Fig. 113), and a finite recti- 

 linear current of length a, and strength I, perpendicular to the first 



A 



a. 



Fig. 113- 



and in the same plane. If we give the current a a displacement 

 doc parallel to the current I, then if r Q is the distance BC, the 

 corresponding work will be 



f r o 



\.'dx\ 



J''o 



1 a 



= 



r 



The force which acts on the movable current is perpendicular 

 to its direction, parallel to the unlimited current, and its value is 



2117. ( i + ). This current will be carried parallel to itself by a 



\ r o/ 



constant force, and will ascend or descend the unlimited current 

 according as it is ascending or descending in reference to this latter. 



The experiment is ordinarily made by causing a circular current 

 to act on a portion of a current movable about an axis perpendicular 

 to its plane and passing through its centre. The movable current 

 then rotates in the opposite direction to the principal current. 



If the movable current is closed, or if its ends are on the axis, 

 there is evidently no movement, for then each line of force meets 

 the edge twice. 



487. ACTION OF A UNIFORM FIELD. Consider first two un- 

 limited rectilinear conductors AA', BB' (Fig. 114) parallel to each 

 other at the distance b, and let us suppose that, while the two ends 

 are in communication with the poles of a battery, the circuit is 

 closed by a cross bar CC', movable parallel to itself along the 

 conductors A A' and BB'. 



Let Z be the component of the intensity of the field perpen- 

 dicular to the plane of the conductors ; for a displacement dx of 



