ich 



360 Prof. G. M. Minchin on the Magnetic 



circles in fig. 2 are marked at the circumferences, and as much 

 of the line of potential belonging to P is drawn as is justified 

 by the number of circles represented in the figure. 



The fundamental proposition of electromagnetism is that 

 the intensity of magnetic force produced at any point in 

 presence of electric currents is the curl of the vector potential 



Fig. 3. 



A P Q B 



at the point. But if in the fie]d there is a current in an in- 

 finitely long straight wire, AB, we find that at every point in 

 the field the vector potential due to this current is infinite. 

 Hence it seems impossible to deduce the magnetic force, and 

 the lines of magnetic force, from the above fundamental pro- 

 position. This result is unsatisfactory, and it manifestly points 

 to some defect in our definition of the vector potential. 



We are presented with a similar unsatisfactory result in the 

 general theory of gravitation potential. Thus, taking the 

 common definition of gravitation potential, if AB is a limited 

 uniform bar attracting according to the law of inverse square, 

 we know that the potential which it produces at any point, 



P, is proportional to log I cot -^ cot -x J, where A=zPAB? 



B= Z.PBA. Now, if the rod extends to infinity, this ex- 

 pression becomes infinite. I have shown (' Statics/ vol. ii. 

 Art. 332) how this difficulty arises, and how it is to be 

 remedied by mending the definition of potential. The diffi- 

 culty is avoided in a similar manner with regard to the vector 

 potential. 



Thus, since we are concerned only with differential co- 

 efficients of the vector potential, the ordinary components, 

 F, G, H of this vector may have added to them any constant 

 quantities whatever. This amounts to saying that the vector 

 potential at any variable point, P, in the field is the vector 

 potential at any fixed point, 0, plus the vector difference 

 between P and 0. It does not matter whether the vector 

 at is infinite or not: it is a constant in the field. As in 

 the general gravitation field we are concerned with differences 





