404 Induced Magnetism [CH. xn 



MECHANICAL FORCES IN THE FIELD. 



471. The mechanical forces acting on a piece of matter in a magnetic 

 field can be regarded as the superposition of two systems first, the forces acting 

 on the matter in virtue of its permanent magnetism (if any), and, secondly, 

 the forces acting on the matter in virtue of its induced magnetism (if any). 



The problem of finding expressions for the mechanical forces in a magnetic 

 field is mathematically identical with that of finding the forces in an electro- 

 static field. This is the problem of which the solution has already been 

 given in 196. The result of the analysis there given may at once be 

 applied to the magnetic problem. 



In equation (117), p. 172, we found the value of E, the ^-component of 

 the mechanical force per unit volume, in the form 



To translate this result to the magnetic problem, we must regard p as 

 specifying the density of magnetic poles, R must be replaced by H, the 

 magnetic intensity, and K by p, the magnetic permeability. Also the 

 electrostatic potential V must be replaced by the magnetic potential H. We 

 then have, as the value of E in a magnetic field, 



30 H z du, 8 {H* 



Clearly the first term in the value of H is that arising from the per- 

 manent magnetism of the body, while the second and third terms arise from 

 the induced magnetism. The first term can be transformed in the manner 

 already explained in the last chapter. It is with the remaining terms that 

 we are at present concerned. These will represent the forces when no per- 

 manent magnetism is present. Denoting the components of this force by 

 E', H', Z' t we have 



-, H* dp 8 



472. This general formula assumes a special form in a case which is of 

 great importance, namely when the magnetic medium is a fluid. 



All liquid magnetic media in which the susceptibility is at all marked 

 consist of solutions of salts of iron, and the magnetic properties of the liquid 

 arise from the presence of the salts in solution. According to Quincke, the 

 solution having the greatest susceptibility is a solution of chloride of iron in 

 methyl alcohol, and for this the value of //, 1 is about T oW*- In such a 

 liquid, the field arising from the induced magnetism will be small compared 



* Cf. G. T. Walker, "Aberration" (Cambridge Univ. Press, 1900), p. 76. 



