CHAP, v.] ELECTRICITY AND MAGNETISM. 273 



an infinite distance on the other ; hence mut represents 

 both the potential of the pole on the shell and the 

 potential of the shell on the pole. Now the lines of 

 force from a pole may be regarded as proportional in 

 number to the strength of the pole, and from a single 

 pole they would radiate out in all directions equally. 

 Therefore, if a magnet-pole was placed at P, at the apex 

 of the solid-angle of a cone, the number of lines of force 

 which would pass through the solid-angle would be pro- 

 portional to that solid-angle. It is therefore convenient 

 to regard ;;zw as representing the number of lines of force 

 of the pole which pass through the shell, and we may call 

 the number so intercepted N. Hence the potential of a 

 magnet-pole on a magnetic shell is equal to the strength 

 of the shell tmiltiplied by the number of lines of force 

 (due to the magnet-pole) which pass through the shell; 

 or V N/. If either the shell or the pole were moved 

 to a point where a different number of lines of force 

 were cut, then the difference of potential would be, 



This formula is of great importance : but the student 

 must be specially cautioned as to the signs to be 

 attributed in applying it to the various quantities. A 

 magnet has two poles, (N.-seeking and S.-seeking) whose 

 strengths are + m and m, and the two faces of a 

 magnetic shell are of opposite sign. To bring up a N.- 

 seeking (or +) pole against the repelling force of the 

 N.-seeking face of a magnetic shell requires a positive 

 amount of work to be done ; and their mutual reaction 

 would enable work to be done afterwards by virtue of 

 their position : in this case then the potential is +. But 

 in moving a N.-seeking pole up to the S.-seeking face of 

 a shell work will be done by the pole, for it is attracted 

 up ; and as work done by the pole may be regarded as 

 our doing negative work, the potential here will have a 

 negative value. 



T 



