276 ELEMENTARY LESSONS ON [CHAP. v. 



the circuit is & Q instead of w p , the potential will have a 

 different value, the difference of potential being, 



V Q - P P = -i (Q - W P ). 



319. (c.) Mutual Potential of a Magnet -pole 

 and a Circuit. If a magnet -pole of strength m were 

 brought up to P, where the circuit subtends a solid-angle 

 w, from an infinite distance against the magnetic forces 

 exercised by the current, m times as much work will be 

 done as if the magnet-pole had been of unit strength, and 

 the work would be just as great whether the pole m were 

 brought up to the circuit, or the circuit up to the pole. 

 Hence, the mutual potential will be 



- mm. 



But, as in Art. 316, we may regard mu as representing 

 the number of lines of force of the pole which are 

 intercepted by and pass through the circuit, and we 

 may write N for that number, and say 



V = - /N, 



or the mutual potential of a magnet-pole and a circuit 

 is eqital to. the strength of the current multiplied by the 

 number of the magnet -pole's lines of force that are inter- 

 cepted by the circuit, taken with reversed sign. 



(</.) As in the case of the magnetic shell, so with the 

 circuit, the value of the potential changes by 407 from a 

 point on one side of the circuit to a point just on the 

 other side ; that is to say, being 2-rz on one side and 

 -f 2in on the other side, work equal to 4^2* must be 

 done in carrying a unit-pole from one side to the other 

 round the outside of the circuit. The work done in 

 thus threading the circuit along a path looped n times 

 round it would be ^niri. 



320. (e.) Mutual Potential of two Circuits. Two 

 closed circuits will have a mutual potential, depending on 

 the strengths of their respective currents, on their distance 

 apart, and on their form and position. If their currents 



