26 ADVANCED ELECTRICITY AND MAGNETISM. 



element of the wire which constitutes the circuit) may be thought 

 of as contributing its share to the field intensity at each point. 

 In fact we have : 



^ (I) 



in which Aff is the field intensity at m in Fig. 21 due to the 

 short piece of wire A/ which is a part of a circuit in which a 

 current of I abamperes is flowing, r is the distance of m from 

 A/, and 6 is the angle shown in the figure; r and A/ are, of 

 course, expressed in centimeters. 



Imagine a magnet pole of strength m placed at the point m 

 in Fig. 21. If we can find an expression for the force exerted on 



direction 



Fig. 21. 

 The field at m due to AZ is at right angles to the plane of the paper. 



A/ by the pole m, we will have an expression for the force 

 exerted on the pole by A/; but the force exerted on m by A/ 

 is equal to the product of m-AH, where A# is the field intensity 

 at m due to A/. 



The field intensity at A/ due to m is -y . The component of 

 this field at right angles to A/ is sin 0, and this component 



pushes sidewise on A/ with a force equal to A/ X / X -7 -sin 

 according to equation (i) of Art. 13; and the force with which 



