261-263] 



Spherical Harmonics 



225 



III. Dielectric sphere in a field of force. 



263. An analogous treatment will give the solution when a homo- 

 geneous dielectric sphere is placed in a permanent field of force. The 

 treatment will, perhaps, be sufficiently exemplified by considering the case 

 of the simple field of potential 



JSmfrnmrO* 

 Let us assume for the potential TJ outside the sphere 



and for the potential TJ inside the sphere 



no term of the form -^ being included in T, as it would give infinite 



potential at the origin. The constants a, /3 are to be determined from 

 the conditions 



These give 



FIG. 78. 



whence 

 so that 



j. 





K-l 



Fx. 



15 



