# Boundary value problem for non-conducting surface

1. Jul 7, 2010

### gaganaut

I have dealt quite a lot with the boundary value electrostatics problem with a plane or spherical conducting surface in an electric field due to a single electric charge or dipole. This can be conveniently done using the method of images. Method of images simplifies a lot of things. Jackson's book has a lot of material on this.

But I have never come across anything like that for non-conducting surfaces, like a wooden plate in an electric field or so. Green's theorem gives the theory for this, but there appears to be no definite solution for this problem. I need to solve this problem for some research, but have hit a major roadblock.

Is this problem of a non-conducting plane surface in an electric field even solvable using a method of images -like formulation? Can some subtle changes in the conducting plane counterpart be made to achieve this particular solution? Can someone direct me to a book or a paper or class notes etc. that solves this problem?

Thanks

2. Jul 8, 2010

### gaganaut

Well never mind. I found a way to find the effect of a dielectric or non-conductive wall on an electric field. It is slightly more involved than its conductive counterpart. Here is a paper that does this derivation http://iopscience.iop.org/0143-0807/21/6/305

It is sort of the like the method of images.

3. Jul 9, 2010

### Born2bwire

I would take a look at Harrington's Moment Method textbook. The method of moments can provide numerical solutions for these kinds of problems. There are of course other methods but in general I think your best bet is to do some form of numerical calculation.