47$ PARTICULAR CASES. 



This latter result would follow directly from a consideration of 

 the equivalent shell. Let 2h be the thickness of the shell supposed 

 to be plane, then denoting by l a the intensity of magnetisation, 



The value of the action of the two terminal layers on a point 

 at the centre is (322) 



and the magnetic induction is 



We may now reject the shell outside the point in question, 

 without changing the value of the force (451). 



494. ELECTROMAGNETIC SOLENOID. Ampere gave the name 

 solenoid to a system of equal circular currents, infinitely near, and 

 infinitely close, equidistant and perpendicular to any given curve 

 passing through their centre, which is called the directrix. 



Let dS be the common surface of the elementary currents, h 

 their distance, and I the strength of the current. Each elementary 

 current may be replaced by a magnetic shell of the same magnitude, 

 of thickness h, and surface density a-, such that we have 



As the surfaces in contact of all these shells have equal and 

 opposite charges, they neutralise each other except at the ends, and 

 the system is identical with that of a solenoidal filament The 

 external action reduces then to that of two magnetic masses M 

 placed at the ends. If / be the length of the solenoid, n the total 

 number of elementary currents, and n : the number of these currents 

 in unit length, we have 



495. CYLINDRICAL COIL. Let us suppose that a cylinder is 

 covered with equidistant currents perpendicular to the axis. The 

 system of these currents forms a kind of cylindrical solenoid, of 



