108 ELEMENTS OF ELECTRICITY AND MAGNETISM. 



When the angle d is equal to 90 (plane of coil at right angles 

 to the field //), then the torque is equal to zero. 



/ - 



/nalff 



lop view 



Fig. 72. 



() Case of a circular coil with its plane parallel to the magnetic field as shown 

 in Fig. 73. In this case let us consider a single turn of the coil of which the radius 

 is r. The vertical dotted line in Fig. 74 represents the axis about which the torque is 

 to be determined. Consider an element A/ of the wire. The component of H 

 which is at right angles to A/ is equal to /if cos <j>, the product //cos <j> X /"X A/ 

 gives the force pushing forwards (towards the reader in Fig. 74) on the element A/, 



two fine suspending 

 wires 



Fig. 73. 



and the product of this force times the lever arm r sin $ gives the torque action on 

 the element A/, that is 



A T= H cos <f> X /X 



but cos ^ X A/ is equal to the vertical height h shown in Fig. 74, so that 

 r sin <f> X cos ' A/ is equal to the shaded area shown in the figure. Therefore, rep- 

 resenting this shaded area by A/*, we have 



