Effective Dielectric constant of two materials

Hi,
The problem is I need to find the surface potential where in the electric fields are elliptic (Fringing fields). I tried to find the solution when there were one dielectric by using con-formal mapping technique which i succeeded. But the problem here is there are two dielectrics
permittivity of 1 >permittivity of 2.
Therefore There is a possible divergence at the interface.
So in order to use con-formal mapping technique i should find effective dielectric constant.
I want to know if there is any of finding effective permittivity between the two perpendicular lines(Yellow marked)

I have attached the picture.

Thanks in Advance