A conducting sphere is kept at potential .
Show that if we embed the sphere in a dielectric that occupies the region
(figure 1, top), the potential
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
change if not the potential of the sphere, but its total charge
is kept at a fixed value?
(Note: Based on 4.35 and 4.36 in Griffiths’s book.)