How Does a Dielectric Half-Space Affect the Potential of a Nearby Point Charge?

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Homework Statement

A point charge q is a distance d from a dielectric half-space (z < 0). We will
solve for the potential outside of the dielectric, in the region z > 0.

(a) Away from the point charge, what equation does V satisfy? Find the bound-
ary conditions at the dielectric surface.

(b) Find an image charge in the dielectric slab that allows you to satisfy the
boundary conditions. What is the potential V outside the dielectric?

(Hint: as epsilon-naught approaches infinity, you should recover the result for a charge next to an infinite
conducting half-space.)

Homework Equations

$$\sigma$$= P dot n = Pz= epsilon-naught*Chi*E

F = 1/(4*pi*ep-naught)*q*qb/(2d)^2=-1/4*pi*ep-naught*(Chi/(Chi+2))*q^2/(4*d^2))

The Attempt at a Solution

I know how to get the potential in the dielectric (Z<0) but I cannot get the potential above Z.


Any help would be greatly appreciated.

 

[gabbagabbahey]

I know how to get the potential in the dielectric (Z<0)

Okay, well how about you start by showing us that then...What does that mean the potential will be at $z=0$?