1 8 ELEMENTS OF ELECTRICAL. ENGINEERING. 



in coil x m/r 2 ; but the length of wire in the coil is 27rrZ, 

 where Z is the number of turns of wire in the coil. Therefore, 



m 2?rZ/ 

 F= I x 27rrZ x -o- = - - X m 



r 2 r 



This is the force with which the test pole acts on the coil of 

 wire. The coil of wire acts upon the test pole with an equal 

 and opposite force, but the force with which the coil acts on the 

 test pole is equal to dfm, where &C is the intensity, at the test 

 pole, of the field due to the coil. Therefore 



or : 



in which c is the intensity in gausses of the magnetic field at the 

 center of a circular coil containing Z turns of wire, r is the radius 

 of the coil in centimeters, and / is the current in the wire in 

 c.g.s. units or abamperes. 



The intensity of the magnetic field at a point in the axis of a circular coil at a 

 distance d centimeters from the plane of the coil is 



27rZr 2 / 



<M = - - (8) 



(r* -4- d*}* 



in which Z is the number of turns of wire in the coil, r is the radius of the coil in 

 centimeters, / is the current strength in c.g.s. units, and d, as above stated, is the 

 distance from the plane of the coil to the point where dt is reckoned. 



Proof of equation (8). Imagine a test pole of strength m placed at the given 

 point. The field intensity at the wire due to this pole is mj(r 2 -\- d 1 }. The compo- 

 nent of this field in the plane of the coil is 



X 



and this component pushes the coil sidewise with a force equal to 



rm 



This same force reacts on the pole and is equal to mcW so that 



