405-408] Magnetic Field of Force 359 



The magnetic force at any point is given, in magnitude and direction, by 

 the force per unit strength of pole, which would act on a magnetic pole situated 

 at this point, the strength of the pole being supposed so small that the magnetism 

 of the field is not affected by its presence. 



408. The other quantities and conceptions follow in order, as in Chapter II. 

 Thus we have the following definitions : 



A line of force is a curve in the magnetic field, such that the tangent at 

 every point is in the direction of the magnetic force at that point (cf. 31). 



The potential at any point in the field is the work per unit strength of pole 

 which has to be done on a magnetic pole to bring it to that point from infinity, 

 the strength of the pole being supposed so small that tJie magnetism of the field 

 is not affected by its presence (cf. 33). 



Let n denote the magnetic potential and a, j3, 7 the components of 

 magnetic force at any point x, y, z, then we have from this definition (cf. 

 equation (6)), 



X '* (330), 



and the relations (cf. equations (9)), 



an an an 



- 



A surface in ike magnetic field such that at every point on it the potential 

 has the same value, is called an Equipotential Surface (cf. 35). 



From this definition, as in 35, follows the theorem : 

 Equipotential Surfaces cut lines of force at right angles. 



The law of force being the same as in electrostatics, we have as the value 

 of the potential (cf. equation (10)), 



n = 2 (332), 



where m is the strength of any typical pole, and r is the distance from it to 

 the point at which the potential is being evaluated. 



As in 42, we have Gauss' Theorem : 



...(333), 



3n 



where the integration is over any closed surface, and 2m is the sum of the 

 strengths of all the poles inside this surface. If the surface is drawn so as 

 not to cut through any magnetised matter, 2m will be the aggregate strength 

 of the poles of complete magnetic particles, and therefore equal to zero. 

 Thus for a surface, drawn in this way 



?dS = 0.. ...(334). 



