and Magnetic Field Constants. 203 



Hence (5) may be written in the form 



V = 2iraa \ e^MXa) J (Xy) ™. . . . (6) 



From this value of V all the results I desire to deal with 

 at present can be derived in succession. 



2. The axially- directed force Z at P due to the disk is 

 — BV/d^, an d therefore by (6) 



('" 

 ^-^J^XaJJolX^rfX. . . (7) 

 «/0 



The force R at P in the direction CP is -dV/dy. 

 Hence remembering that J '(\^) = —J 1 (Xi/) we obtain 



/l oo 



R, = 27r*a\ e-^JiiXa^JiiXyjdX. . - (8) 



Case (2). A circular doublet-disk (a circular magnetic 

 shell) of uniform strength m per unit area is placed 

 with its centre at 0, its axis along 00, and its positive 

 side turned towards : it is required to find in terms 

 of Bessel functions the potential produced at P and the 

 component magnetic field intensities. 



It is required also to show that, if A be a point on 

 the circle of centre and radius a, the axially directed 

 magnetic field intensity at P is equal to the radial or 

 ^/-component of the electric intensity at A due to a 

 parallel uniformly electrified circular ring (centre 0). 



Olearly —'dY/'dz.dz is the potential at P due to such 

 a doublet-disk, if m = cdz. Calling this potential XI, we 

 obtain from (7) 



(AGO 

 e~ Xz 3i(\a)3 (X.y)d\. ... (9) 



The forces Z and R for this magnetic shell are given by 



r\ oo 



Z = 2irma\ e~ Kz J x (Xa) J {\y)\d\j ) 



Obviously if this doublet-disk have its centre at C, i/( = />) 

 for its radius, and 0( ) for its axis, and face in tha same way 



F2 



