28 



ADVANCED ELECTRICITY AND MAGNETISM. 



with their centers on the axis of the wire. The intensity of the 

 field at the point m in Fig. 23 can be determined by integrating 



wire 



wire 



magnet 



Fig. 23. 

 The field at m due to A* is directed towards the reader. 



equation (i) of Art. 18 as follows: Substitute Ax for A/, sub- 



D 

 stitute (D 2 + x 2 ) for r 2 , and substitute 



X 2 



for sin 6. 



Equation (i) of Art. 18 then becomes: 



Ax 



AH = ID 



(D 2 



(i) 



Therefore, by integrating between the limits x = oo to 

 x = + we have: 



H = % (2) 



Thus at a distance of 10 centimeters ( = D) from a long straight 

 wire carrying a current of 50 abamperes ( = /) the intensity of 

 the magnetic field is 10 gausses (='H). 



20. Torque exerted on a coil which is suspended in a uniform 

 magnetic field. Case I. Rectangular coil with two of its edges 

 parallel to the field as shown in Fig. 24. The forces FF in Fig. 24 

 are each equal to IZ X / X H according to equation (i) of Art. 13, 

 where / is the dimension shown in Fig. 24, Z is the number of 



