4 ADVANCED ELECTRICITY AND MAGNETISM. 



a force of one dyne on each unit of m" . Thus if w' = 3 units 

 and m" = 2 units, then the force of attraction or repulsion will 

 be six dynes, as indicated in Fig. 3, where each dotted line rep- 

 resents one dyne. 



7. Complete expression for the force of attraction or repulsion 

 of two magnet poles. Coulomb discovered in 1800 that the force 

 of attraction or repulsion of two magnet poles is inversely pro- 

 portional to the square of the distance between them (Coulomb's 

 law). But the force of attraction or repulsion of two magnet 

 poles when they are one centimeter apart is m'm" dynes as 

 explained in Art. 6. Therefore, according to Coulomb's law, 



the force of attraction or repulsion is - dynes when the poles 

 are r centimeters apart. That is : 



!--= M 



in which m' and m" are the respective strengths of two magnet 

 poles, r is their distance apart in centimeters, and F is the force 

 in dynes with which the poles attract or repel each other. 



Algebraic sign of magnet pole. It is customary to consider a 

 north pole as positive and a south pole as negative. That is, 

 m is positive when it expresses the strength of a north pole and 

 negative when it expresses the strength of a south pole. There- 

 fore, the product m'm" is positive when both poles are north 

 poles or when both poles are south poles, and in this case the 

 force F in equation (i) is a repulsion. The product m'm" is 

 negative when one pole is a north pole and the other pole is a 

 south pole, and in this case the force F in equation (i) is an 

 attraction. Therefore, when F in equation (i) is positive it is 

 a repulsion, and when it is negative it is an attraction. 



8. Direction and intensity of a magnetic field at a point. 

 A magnetic field may be defined as a region in which a suspended 

 magnetic needle tends to point in a definite direction, and the 



