vector potential problem

[Tor Fredrik]

 

 

In the example 5.11 above I don't understand how they revert to the natural coordinates while going from (5.68) to (5.69). In (5.68) the direction is along the y-axis. In (5.69) it follows the angle that goes round the sphere. But this angle is normal to y when it is at the y axis and parallell to the y axis while it is at the x-axis. How is it possible to revert between the y-axis in (5.68) and the angular axis in (5.69)? 

 

Edited December 13, 2019 by Tor Fredrik