CHAPTER XVII 

 THE INVERSE SQUARE LAW 



Variation of the force due to a pole as the distance from the pole is 

 varied The inverse square law Magnetic measurements founded on the 

 law Coulomb's experiments Unit magnetic pole Strength of pole m 

 Magnetic intensity Geometrical construction for the direction of the 

 intensity in the field of a har magnet Gauss's proof of the inverse 

 square law Deflection method of verification Moment of a magnet 

 Comparison of moments Some consequences of the inverse square law 

 Application of Gauss's theorem Flux of force Unit tube? A pole 

 m sends out 4ir m unit tubes Potential. 



Variation of the force due to a pole as the distance 

 from the pole is varied. The inverse square law. If a 



NSP is placed at any point in the field of a magnet, the force on it 

 is due to the action of the magnet as a whole. We cannot isolate 

 one of the two polarities. Always the two come into play and the 

 action is the resultant of the North-seeking repulsion and the South- 

 seeking attraction. The best approach we can make to isolation of 

 one polarity consists in so arranging the acting magnet that one 

 pole has practically very little action as compared with the 

 other. 



Coulomb's experiments. This method was used by 

 Coulomb, to whom we owe the decisive experimental proofs which 

 finally established the inverse square law.* In one experiment he 

 used a steel wire magnet 25 inches long. He first found that the 

 poles might be considered an inch from each end. Then, placing 

 the wire vertically, he noted the time of vibration of a needle 

 opposite the lower pole and at different small distances from it in 

 the plane of the magnetic meridian. The upper pole was not onlv 

 at a much greater distance, but its action was nearly vertical, so that 

 for two reasons the horizontal component of the force due to it 

 was sufficiently small to be negligible. 



It was necessary to take into account the action of the earth 

 which was added to that of the magnet in all cases. Let us 

 suppose that the horizontal force on each pole of the needle due to 

 the earth is H r and that the force due to the pole of the magnet at 

 distance d is F x and at distance d 2 is F 2 , and let the times of 



* For a history of the experiments made by Coulomb's predecessors, sec 

 Brit. 9th ed., Magnetism, p. 236. 



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