CHAF. v.] ELECTRICITY AND MAGNETISM. 275 



preceding paragraphs derive their great importance 

 because of the fact laid down in Art. 192 that circuits, 

 traversed by currents of electricity, behave like magnetic 

 shells. And for the purpose of calculating the magnetic 

 effects due to currents by applying these theorems, it is 

 necessary to adopt the electromagnetic unit of the 

 strength of current explained in Art. 196. If we adopt 

 such a unit we may at once go back to Art. 315, and 

 take the theorems about magnetic shells as being also 

 true of closed voltaic circuits. 



(a.) Potential due to closed circuit (compare 

 Art. 315). 



The potential V due to a closed voltaic circuit (traversed 

 by a current) at a point P near it^ is equal to the strength 

 of the current multiplied by the solid- angle w subtended 

 by the circuit at that point. If i be the strength of the 

 current in electromagnetic units, then 



V P = - tat. 



The reason for adopting the negative sign is the following : 

 The potential (i.e. the work done on a unit N. -seeking 

 pole) is reckoned positive where the work is done 

 against repulsion. Now, if a N. -seeking pole is to be 

 brought up to a point opposite the repelling face of a 

 circuit, it must (see Fig. 115) be brought up to that face 

 round which the electricity is flowing in the counter- 

 clock-wise or negative direction, or round which the 

 current must be considered as having strength = i. 

 The student may be helped to understand this conven- 

 tion about signs by remembering (see Fig. 115) that 

 when he is looking at the S. -pole of an electromagnet 

 he is looking along the magnetic lines of force in their 

 positive direction, and that the current is running clock- 

 wise round the coil. Or, the positive direction of lines 

 of force through the circuit is associated with a (positive) 

 rotation round the circuit, as is the forward thrust with 

 the right-handed rotation in the operation of driving an 

 ordinary right-handed screw. 



(b.) At a point Q, where the solid-angle subtended by 



