1872.] Prof. J. C. Maxwell on Electric Induction. 



163 



1 1 . It appears from this that, when the electromagnet is increasing in 

 intensity, it will be acted on by a repulsive force from the sheet, and when 

 its intensity is diminishing, it will be attracted towards the sheet. 



It also appears that if any system of currents is produced in the sheet 

 and then left to itself, the effect of the decay of the currents, as observed at 

 a point on the positive side of the sheet, will be the same as if the sheet, 

 with its currents remaining constant, had been carried away in the negative 

 direction with velocity R. 



12. If a magnetic pole of strength m is brought from an infinite distance 

 along a normal to the sheet with a uniform velocity v towards the sheet, 

 it will be repelled with a force 



?n 2 v 



where s is the distance from the sheet at the given instant. 



This formula will not apply to the case of the pole moving away from 

 the sheet, because in that case we must take account of the currents 

 which are excited when the pole begins to move, which it does when near 

 the sheet. 



13. If the magnetic pole moves in a straight line parallel to the sheet, 

 with uniform velocity v, it will be acted on by a force in the opposite direc- 

 tion to its motion, and equal to 



m 2 js/W + v' + R-v 



Besides this retarding force, it is acted on by a force repelling it from 

 the sheet, equal to 



2 2 



m v 

 4^R 2 + W 2 + RVR 2 T^ 2 ' 



14. If the pole moves uniformly in a circle, the trail is in the form of a 

 helix, and the calculation of its effect is more difficult ; it is easy, how- 

 ever, to see that, besides the retarding force and the repelling force, there 

 is also a force towards the centre of the circle. 



15. It is shown, in my treatise on Electricity and Magnetism (vol. ii. 

 art. 600), that the currents in any system are the same, whether the con- 

 ducting system or the inducing system be in motion, provided the relative 

 motion is the same. Hence the results already given are directly appli- 

 cable to the case of Arago's rotating disk, provided the induced currents 

 are not sensibly affected by the limitation arising from the edge of the 

 disk. These will introduce other sets of images, which we shall not now 

 investigate. 



16. The greater the resistance of the sheet, whether from its thinness 

 or from the low conducting-power of its material, the greater is the velocity 

 R. Hence in most actual cases R is very great compared with v, the 

 velocity of the external system, and the trail of images is nearly normal to 



