# Electromagnetics - parallel plates (Poisson/Laplace)

1. Sep 30, 2006

I'm not sure where to post this. It's for an engineering class, but it's more a question about the math.

I'm following an example along in my book, and I just need a little help understanding it:

(Q)
There are two plates of a parallel-plate capacitor that are separated by a distance d and maintained at potentials 0 and V0. Assume neglible fringing effect at the edges, determine (a) the potential at any point between the plates, and (b) the surface charge densities on the plates.

(A)
So the book says,

Laplaces equation is the governing equations for the potential between the plates since $\rho = 0$.

Ok, so if we can solve $$\nabla^2 = -\frac{\rho}{\epsilon}$$ then we have found an expression for the voltage. So the book says that there is zero charge between the sheets. So my question comes from this.

Since zero charge is between the sheets, Poisson's equations becomes Laplaces equation. Now when we solve Laplaces equation does this mean it is only valid between the sheets? Since we are saying that $\rho = 0$ aren't we restricting our domain to values that are NOT on the sheets themselves?

Why would be allowed to use:
$$v(x,y,z=0)=0$$
and
$$v(x,y,z=d) = V_0$$

as boundary conditions, when we are assuming $\rho = 0$.

Does that make sense as a question?