204 



Prof. A. Gray on Electric 



as the disk just considered, the magnetic force at A in' the- 

 direction OC is by (10) 



r»ao 



27rmh\ e-^J^X^J^X^XdX. 



Jo 



• (ii) 



But going back to (5) we see at once that the potential at A 

 due to a uniform ring, centre C, of electricity (or matter) of 

 uniform linear density [jL<=o-p, and of radius p = b, is 



i 



2t7y«j <?- a 'J„(X?')J (\'/)(/X. . 



(12) 



The field intensity at A in the direction of y is — BV/dy, 

 or if we call it R/, 



R' = 27r/x«( e-^JoiUyJ^X^XdX, . . (1 



3) 



which, with p, = ma/b, is by (10) exactly the field intensity Z 

 at P due to the magnetic disk centre 0, but turned through 

 a right angle. This is an example of the theorem of reci- 

 procity of magnetic and electric field intensities at corre- 

 sponding points stated in my paper (Phil. Mag. May 1919). 

 A similar result can be obtained for the other component. 



Case v (3). A uniform right circular cylinder of volume 

 density p (of electricity or ordinary matter) has its 

 axis along OC, and its right-hand end (fig. 2) at r 

 required the potential and the field intensities in terms 

 of Bessel functions. 



Fio-. ± 





We write pclz for a and integrate (6) from the end nearer 

 to the end further from C. It" we now suppose z to be the- 



