37^ MAGNETIC INDUCTION. 



value of the force is a maximum. A very small magnetic body in a 

 variable field tends then to move towards points where the force is a 

 maximum. As there is no absolute maximum of force outside 

 acting masses (180), it follows that, if the body is left to itself, it 

 will end by touching the surface of the magnets ; it is therefore 

 attracted by the magnets. 



For diamagnetic substances the coefficient k is negative. A small 

 diamagnetic body approaches points where the force is a minimum ; 

 it tends to move more and more away from the centres of force it is 

 repelled by magnets. 



As the field may contain points where the force is null, and which 

 are then absolute minima for the value of </> 2 , we see that there may 

 be stable equilibrium for a diamagnetic body in a variable field 

 outside acting masses. 



Faraday had already announced as a result of experiment this law, 

 that magnetic bodies move towards points where the force is a maximum, 

 and diamagnetic bodies towards points where the force is a minimum. 

 It is to Sir W. Thomson that we owe the true interpretation of the 

 phenomenon. 



In a uniform field the energy of a small isotropic, magnetic, or 

 diamagnetic body is constant, and therefore the force null. 



396. For an anisotropic magnetic body the total energy is the 

 sum of the energies corresponding to the magnetic moments u$>k\, 

 u<}>k'X', &<>"A", due to the components <A, <A', </>A" of the force 

 parallel to the three axes ; we have then 



W = - u (ktf + k'X'* + k" A" 2 ) . 



If the body is compelled to turn about its centre of gravity, 

 stable equilibrium corresponds to the case in which the energy is a 

 minimum that is to say, where the expression comprised between 

 the brackets is a maximum. 



As it is necessary, for equilibrium, that two of the cosines A, A' 

 and A" are zero, this maximum will take place when the quantity in 

 brackets is reduced to the term corresponding to the greatest of the 

 coefficients k, k' and k". The axis of greatest magnetisation is then 

 parallel to the force of the field. 



If a body passes from a position in which the force and the 

 direction of the field are defined by < 1? A 19 A\, A" 3 , to another 



