Infinite line charge and parallel conducting cylinder
We have considered the problem of a line charge of density 
C/m located at a distance d from the axis of a parallel conducting cylinder of radius a. We assume both the cylinder and the line charge to be infinitely long.
Since the cylindrical surface at a radial distance a from origin O is an equipotential surface, the image charge is a parallel line charge inside the cylinder. We are to determine the image charge density 
and the location of the image charge d' from O. Let us assume 
. The electrical potential at a distance r from an infinite line charge of density can be written as
where 
is the reference point of zero potential. [Note that, for the present case cannot be infinity.]