A conducting sphere is kept at potential V 0. Show that if we embed
the sphere in a dielectric that occupies the region z < 0 (figure 1, top),
the potential V (r) will stay exactly the same everywhere in space as
in the absence of the dielectric! What about configurations (a) and (b)
(figure 1, bottom)?
How will V (r) change if not the potential of the sphere, but its total
charge Q is kept at a fixed value?
(Note: Based on 4.35 and 4.36 in Griffiths’s book.)
|Figure 1: ||A conducting sphere embedded in a dielectric in various ways.|