356 PARTICULAR CASES. 



If the magnet is a ring of revolution, and x is the radius of an 

 elementary solenoid, we shall have 



A (Vs A (Vs 



Q = 4?rA = 2 A . 



J 2TTX J X 



Consider a torus or anchor ring, for instance. Let a be the 

 radius of the section and R the distance of its centre from the axis 

 of rotation taken as axis of z; we have then 



and the value of the total flow of induction is 



() Q 



373. CYLINDER. A cylinder uniformly magnetised and termi- 

 nated by right sections, is equivalent to two equal and opposite 

 magnetic layers 1, which cover the two bases A and B. The 

 potential of any such magnet at a given point is equal to the 

 sum of the potentials V a and V & , of the two terminal layers. 



If the right section of the cylinder is circular, the potentials 

 V a and V 6 may be expressed by the formulae found previously 

 (365 and 366). 



The expression for the magnetic force on a point M of the axis 

 on the outside and on the side of the positive face A, is 



F=27rl(i -COS a)- 27rl(i - COS fi) = 27rl(cos ft - COS a), 



a and /? being the angles under which the radii of the two bases are 

 seen from the point M, and it is in the same direction as that of the 

 magnetisation. 



For a point in the interior, the actions of the two bases are of the 

 same sign, which gives a force 



F = 4?rl - 2?rl (cos a + cos ft), 

 in the opposite direction of that of the magnetisation. 



