in an Infinite Plane Current Sheet. 143 



whose axis is parallel to the axis of revolution, and whose 

 positive pole is situated at a point whose coordinates arez=/*, 

 p = c, <f> = : and let us find the magnetic potential of the 

 currents, when the magnet is rotating about the axis of z, in 

 the same direction as that in which c/> is measured. 

 In this case, 



n/ = ™ 



\ + Er + lif + p 2 + e 2 - 2pc cos(0 + «t) p j 



where m is the strength of the positive pole ; whence by (8), 



;1 



Let 



Q = ^ 2 + c 2 — 2pc cos (<£ + cot) p ; 

 Then, since 



and 



Jo(^Q) = Jo (V) Jo(^) + 2Sr J«(ty) J» (Xc) COS 71 (0 + cot), 



the value of O becomes 



°=" 2mft, ^J ^£ ^ AU+RT+A) 2rJ^)J»(Xc)cosn(^H-a)T)^ 



= 2im»S I nJ a EV + nV *-^dk. (9) 



The forces which act on the pole are given by the fol- 

 lowing equations : — 



Ida 2mR y 2 f" Xe- 2AA 



c 2,n ) E^?+^W J -( Xc )^ 



Kio) 



= — 2mco 2 Xn 2 I R2 ^ 2 . 2q)2 J/ « (Xc) J w (Ac)rfX. 



c rfc£ 



Now we have supposed the magnetic pole to be rotating in the 

 same direction as that in which d> is measured, therefore the first 

 equation indicates a force tending to oppose the motion of the 

 magnet ; hence the magnet exerts a force on the sheet tending 

 to pull it round in the direction of rotation. If therefore the 

 magnet is fixed and the sheet be made to rotate, the magnet 

 will experience a dragging force parallel to the direction of 

 motion of the sheet. 



