PART III. 



THE MAGNETIC REACTIONS PRODUCED BY A COPPER DISK 

 ROTATING BETWEEN THE POLES OF A MAGNET. 



That a rotating disk exerts not merely a tangential drag, but also a 

 repulsive force, on a magnet pole placed near it, has been known since 

 the days of Arago. 1 Nobili 2 first discovered that the loops of induced 

 current are displaced in the direction of rotation of the disk, though he did 

 not understand the part played by self-induction in causing this. Indeed, 

 as far as we are aware, no attempt has been made up to the present time to 

 make a quantitative determination of the electric and magnetic effects. 



Mathematically, the problem of the currents induced in bodies rotating 

 in a magnetic field has been attacked by Felici, Jochmann, Maxwell, 

 Himstedt, Niven, Larmor, Gans, and especially by Hertz. 3 The chief 

 results of Hertz's work that have a bearing on the present paper may be 

 summarized as follows: When a conducting mass is rotated in a mag- 

 netic field, the induced currents, owing to self-induction, are distorted 

 in the direction of rotation to an extent independent of the intensity 

 of the magnetic field but increasing with the angular velocity. At the 

 surface of the conductor the currents are less distorted than in the interior. 

 At infinite angular velocity the surface of the conductor would act toward 

 magnetic forces like a conducting surface in an electric field, screening 

 the interior entirely from all magnetic action. 



These mathematical investigations were all made on the assumption 

 of certain ideal conditions, which in general it would be hard to realize 

 experimentally. In order to apply theoretical principles at all to the 

 present case it is necessary to make some simple assumptions and to be 

 content with qualitative relations. The problem would be comparatively 

 simple if the disk were so thin that it could be regarded as a current sheet, 

 if the magnetic induction B were uniform in the space between the poles, 

 and if the self-induction of the disk could be neglected. Calling co the 

 angular velocity of the disk, 4 we would then have for the induced electro- 

 motive force 



e = constant x w B 



1 Arago, Pogg. Ann., 1826, 7, p. 590; Pohl, Pogg. Ann., 1826, 8, p. 369. 



2 Nobili, Pogg. Ann., 1833, 27, p. 401. Avery full account of the classical experi- 

 ments on rotating disks is given in Wiedemann's "Galvanismus und Elektromagnetis- 

 mus," Braunschweig, 1874. 



3 Felici, Annali di sci. mat. e fis., 1853, p. 173; Jochmann, Pogg. Ann., 1864, 122, p. 

 214; Maxwell, "Electricity and Magnetism," 2, p. 300; Himstedt, Wied. Ann., 1880, 

 11, p. 812; Niven, Proc. Roy. Soc. 30, 1880, p. 113; Larmor, Phil. Mag. (5), 1884, 17, 

 p. 1; Gans, Zschr. f. Math. u. Phys., 1902, 48, p. 1; Hertz, Inaugural Dissertation, also 

 "Gesammelte Werke," 1, 1895, p. 37. 



4 In Parts I and II speeds were expressed in revolutions per minute of the pedals, 

 because in using the bicycle ergometer this is the important quantity. Since in Part 

 III attention is centered chiefly on the disk, we shall, in what follows, in general refer 

 to the angular velocity or number of revolutions per minute of tne disk, obtained by 

 multiplying all pedal speeds by 3.25, the ratio of the two sprocket-wheels. 



31 



