184 ON FARADAY'S LINES OF FORCE. 



Ampere has shewn that when currents are combined according to the law 

 of the parallelogram of forces, the force due to the resultant current is the 

 resultant of the forces due to the component currents, and that equal and 

 opposite currents generate equal and opposite forces, and when combined 

 neutralize each other. 



He has also shewn that a closed circuit of any form has no tendency to 

 turn a moveable circular conductor about a fixed axis through the centre of 

 the circle perpendicular to its plane, and that therefore the forces in the case 

 of a closed circuit render Xdx+ Ydy + Zdz a complete differential. 



Finally, he has shewn that if there be two systems of circuits similar 

 and similarly situated, the quantity of electrical current in corresponding 

 conductors being the same, the resultant forces are equal, whatever be the 

 absolute dimensions of the systems, which proves that the forces are, cceteris 

 paribus, inversely as the square of the distance. 



From these results it follows that the mutual action of two closed currents 

 whose areas are very small is the same as that of two elementary magnetic 

 bars magnetized perpendicularly to the plane of the currents. 



The direction of magnetization of the equivalent magnet may be pre- 

 dicted by remembering that a current travelling round the earth from east 

 to west as the sun appears to do, would be equivalent to that magnetization 

 which the earth actually possesses, and therefore in the reverse direction to 

 that of a magnetic needle when pointing freely. 



If a number of closed unit currents in contact exist on a surface, then at 

 all points in which two currents are in contact there will be two equal and 

 opposite currents which will produce no effect, but all round the boundary of the 

 surface occupied by the currents there will be a residual current not neutralized 

 by any other ; and therefore the result will be the same as that of a single 

 unit current round the boundary of all the currents. 



From this it appears that the external attractions of a shell uniformly 

 magnetized perpendicular to its surface are the same as those due to a current 

 round its edge, for each of the elementary currents in the former case has 

 the same effect as an element of the magnetic shell. 



If we examine the lines of magnetic force produced by a closed current, 

 we shall find that they form closed curves passing round the current and 

 embracing it, and that the total intensity of the magnetizing force all along 

 the closed line of force depends on the quantity of the electric current only. 



