= M1 



Figure 217 - Point dipole /x, either outside 

 or inside of a fixed spherical surface. 

 See Section 131. 



x-b^ f \ 3 _.2 



X - br. 



, xp = - H^cu' 



[131f,g] 



Here ip is given by Equation [131a], with k tai<en from Equation [131e], and (f> is found by 

 comparison with Equations [119k] and [119o]. 



The velocity at any point can be found by adding vectorially the velocities due to 

 the two dipoles. 



On the sphere itself r /r = a/b. by similar triangles, hence i/» = and 



,2 A 2 



^ Ml 



a^ - b: 



, fj = {a^ + 6j - 2 ab^ cos (9)'/% 



where 6 is the polar angle at the center measured from a line through the dipole. Thus on 

 the sphere 



1 ^c6 TO sin d 



[131h] 



and, since the velocity is tangential to the sphere, q = \qn\ 



328 



