and Magnetic Field Constants, 



209 



required to find the. surface integral of potential over a 

 circle of radius a concentric with the disk, and coinciding 

 -with the face of it. It is supposed that b >a. 



Fijr. 4. 



Consider a point P at distance / from the centre 0, 

 and denote the angle 0PM by -v/r. Taking the disk as of 

 unit surface density, we get for the potential V at P 



V = 2 



1 r dyjr. 

 Jo 



(28) 



The integral of this over a small area jdfd<j> at P is 

 V fdfd<j>. Hence for the integral over the circle of radius a 

 we have 



I = 4w\"i "rfdfdf, 



(29) 



'o 'o 



for it is clear that the potential at the point P is also the 

 potential at every point on a circle of radius / described 

 about the centre of the disk. 

 We have to calculate 



i7T -\ a 



I frdfdyfr. 



Jo J« 



