480 PARTICULAR CASES. 



All the elementary solenoids comprise then the same number of 

 currents with the same intensity I, but of different lengths. If n^ 

 is the number of windings comprised between two meridian planes 

 which make with each other an angle equal to unity, and if x is the 

 radius of an elementary solenoid, the distance of the successive turns 



will be ; the intensity of magnetisation of the equivalent magnetic 



filament is then 2L , and the induction, or the magnetic force, ^ HI . 



x x 



The value of the flow of induction across a surface S, taken in the 



/ 7Q 



meridional section of the ring, is 473-^1 . 



J x 

 In the case in which the ring is a circular torus (372), we have 



--WR 



x 



The total flow across the section is then 



497. CASE OF ANY GIVEN SURFACE. Let us now consider the 

 general case in which any surface J5f is covered by plane currents of 

 the same strength, parallel to each other, and at such a distance that 

 these are n^ in unit length. These currents may be replaced by a 

 series of parallel solenoids terminating in the surface, and these 

 solenoids themselves by equivalent magnetic filaments ; in this way 

 a uniform magnet will be formed, the intensity of magnetisation 

 of which is n^, and the density at each point of the surface, has 

 the value n-J. cos 0, where 6 is the angle which the perpendicular to 

 the surface, at the point in question, makes with a perpendicular to 

 the plane of the currents. 



The internal action of these currents is equal to the induction of 

 the equivalent magnetic system. In the case of the sphere (355) it 



o 



is constant and equal to -irn-^L ; the value of the flow of induction 



across the great circle perpendicular to the line of- the poles on the 

 common axis of the currents is 



where L is the circumference of the great circle. 



