278 Dr. R. A. Lehfelclt on the 



In the same way it may be shown that for a point in the 



?' dA. 

 plane of the elementary circuit the field dH=— — . 



The product idk. may then be defined as the magnetic 

 moment of the elementary circuit. 



It is easy to show that, for a point in any direction, the 

 area — or magnetic moment — of the elementary circuit may 

 be resolved into axial and equatorial components, and the 

 effect of the two parts calculated according to the preceding- 

 rules. We have, thus, a complete picture of the magnetic 

 field round an element of a circuit. 



The next step is to show that the field can be derived from 

 a potential. The necessary integration is given in all treatises 

 on electricity, and shows that the magnetic potential in the 

 axial direction has the value 



while in the equatorial direction it vanishes ; and at any 

 point making an angle % with the axis of the elementary 



circuit the magnetic potential is c?X2= — 2~cos %. Now the 



solid angle subtended by the circuit at the point is 



dA 



— — cos % = dw. Hence d£l = i dw. If, however, this relation 



is integrated, bearing in mind the way in which a circuit 

 may be supposed built up of small plane elements, the sides 

 of which cancel in their magnetic effects (as demonstrated by 

 Ampere) we conclude that 



that is, the magnetic potential produced by a current is 

 equal to the strength of the current multiplied by the solid 

 angle subtended by the circuit in w T hich it flows. 



It then follows, by considering the changes of magnetic 

 potential along any closed path, that 



the first circuital relation of electrodynamics. 



At this point it is convenient — still considering non- 

 magnetic media — to calculate the field in the interior of a 

 solenoid, either infinitely long or finite, and, if desired, to 

 calculate the forces and couples exerted on circuits — plain or 

 solenoidal — when placed in a magnetic field. 



It may then be pointed out that, on the view that magnets 



