# Induced Charge on Conducting Surface

I am making my way through Griffiths' Introduction to Electrodynamics and ran across the following passage:

Suppose a point charge $$q$$ is held a distance $$d$$ above an infinite grounded conducting plane. What is the potential in the region above the plane? It's not just $$(1/4\pi\epsilon_0)q/r$$, for $$q$$ will induce a certain amount of negative charge on the nearby surface of the conductor...

Later on, Griffiths states the boundary conditions for which we must solve Laplace equation:

1. $$V=0$$ when $$z=0$$ (since the conducting plane is grounded), and 2
2. $$V \rightarrow 0$$ far from the charge.

I understand that the electric field inside a conductor is zero, and that specifying that the conductor is grounded is synonymous with stating $$V=0$$, and that any induced charge will be on the boundary of that conductor. But in the case of a grounded plane, would the boundary not be the plane itself, such that $$V\neq 0$$? Where else would the induced charge that Griffiths refers to reside?

You should look up method of images for a conducting plane.