THE MAGNETISM OF IRON. 73 



41. Behavior of a magnet in a uniform magnetic field. A bar 

 of steel weighs the same before and after being magnetized 

 (earth's field being uniform), and the fiber by which a magnet is 

 suspended hangs vertically (earth's field being uniform). Any 

 force tending to produce translatory motion of a magnet would 

 cause it to weigh more or less after magnetization than before, 

 or would tend to cause a suspending fiber to be out of plumb. 

 Therefore the forces with which the uniform magnetic field of the 

 earth acts upon a magnet do not tend to produce translatory 

 motion, the force which acts on the north pole of the magnet is 

 equal in value and opposite in direction to the force which acts 

 upon the south pole of the magnet, as indicated in Fig. 38,' and 

 therefore the poles of the magnet are equal in strength and 

 opposite in sign. 



Consider a magnet of length / placed in a uniform magnetic 

 field of intensity H, the angle between the axis of the magnet 

 and the direction of the 

 field being 0, as shown in 

 Fig. 38. The poles of the 



magnet are acted upon by /& \ lines of force 



$r * of field H 



the forces -f mH and 



mH, respectively, the mo- 

 ment of each of these forces 



Fig. 38. 



about the center of the 



magnet is equal to mH x //2 x sin 6, and both of these moments 

 tend to turn the magnet in the same direction. Therefore the 

 total torque T tending to turn the magnet into the direction of 



the field is 



T=-mlHsm0 (21) 



The negative sign is chosen simply for the reason that the torque 

 tends to reduce 6 which may be considered as a positive angle. 

 This equation expresses the torque in dyne-centimeters. When 

 the angle 6 is equal to zero or 180, the torque T is zero and 

 the forces + mH, mH have no tendency to turn the magnet, 



