In the book titled "Modern Electrodynamics" by Zangwill, on chapter 8, there is a discussion on the electric potential of a system of an infinite conducting plane and a point charge described by the image below.
Notice that the charge itself is in region $V$ but its image is in region $V'$. It is pretty clear and written in almost every textbook that what the potential will be in region $V$. Zangwill writes:
The [image charge] method tells us nothing about the potential in $V'$
So my question is, what is the potential in region $V'$ and how can we find it?
Best Answer
I figured out the answer. Since the conductor is infinite, the surface charge density induced by the point charge on the conductor will be $\sigma=\frac{Q}{A}=0$. Hence, the potential due to this charge distribution in region $V'$ will be zero.