How Do You Solve for the Potential Outside a Dielectric Half-Space?

[Einsteinium1]

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 boundary 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 $$\epsilon$$ -> $$\infty$$, you should recover the result for a charge next to an infinite conducting half-space.

I'm pretty lost with this question. Any hints starting the problem would be very helpful. Thank you.

 

[nickjer]

(a) is pretty simple. In free space, what equation do you use for the potential?

You can get the BC's from Gauss's law and Faraday's law for the electric field. Then convert those to BC's for the potential.