Electric potential due to an infinite conducting cylinder with internal or external point charge

We utilize the Greenʹs function method in order to calculate the electric potential due to an infinite conducting cylinder held at zero potential and a point charge inside and outside it. We calculate and plot the net force upon the point charge as a function of its distance to the axis of the cylinder. We show that this force goes to zero when the radius of the cylinder goes to zero, no matter the distance of the external point charge to the conducting line.