12 



Electrostatics Physical Principles 



[OH. i 



condition for equilibrium is obviously that there shall be no torsion in 

 the thread. If, however, we fix a third small ball E in the same plane as 



the other two, and if the three balls are elec- 

 trified, the forces between the fixed ball and 

 the movable ones will exert a couple on the 

 moving rod, and the condition for equilibrium 

 is that this couple shall exactly balance that 

 due to the torsion. Coulomb found that the 

 couple exerted by the torsion of the thread 

 was exactly proportional to the angle through 

 which one end of the thread had been turned 

 relatively to the other, and in this way was 

 enabled to measure his electric forces. In 

 Coulomb's experiments one only of the two- 

 movable balls was electrified, the second serv- 

 ing merely as a counterpoise, and the fixed 

 ball was at the same distance from the torsion 

 thread as the two movable balls. 



Suppose that the head of the thread is 



turned to such a position that the balls when uncharged rest in equilibrium, 

 just touching one another without pressure. Let the balls receive charges 

 e, e, and let the repulsion between them result in the bar turning through 

 an angle 0. The couple exerted on the bar by the torsion of the thread 

 is proportional to 0, and may therefore be taken to be icO. If a is the 

 radius of the circle described by the movable ball, we may regard the couple 

 acting on the rod from the electric forces as constituted of a force F, equal 

 to the force of repulsion between the two balls, multiplied by a cos ^6, 

 the arm of the moment. The condition for equilibrium is accordingly 



Let us now suppose that the torsion head is turned through an angle <j> 

 in such a direction as to make the two charged balls approach each other ; 

 after the turning has ceased, let us suppose that the balls are allowed to 

 corne to rest. In the new position of equilibrium, let us suppose that the 

 two charged balls subtend an angle & at the centre, instead of the former 

 angle 0. The couple exerted by the torsion thread is now K (0' + </>), so that 

 if F' is the new force of repulsion we must have 



CL* 7 ' cos 0' = 



By observing the value of </> required to give definite values to & we can 

 calculate values of F' corresponding to any series of values of 6'. From a 

 series of experiments of this kind it is found that so long as the charges on 

 the two balls remain the same, F' is proportional to cosec 2 ^#', from which 

 it is easily seen to follow that the force of repulsion varies inversely as the 



